in the short history of mankind the majority of the tools which man is made can be thought of as an extension of his muscle power that is the ability to perform work faster and in greater qu is the electronic computer it is the fast reliable and tireless performance of the variety of arithmetic mind you can operation give the computer its great utility and power but merely looking at a computer won't tell us very much about what it actually is we know that the modern jet aircraft represents a great increase in speed over the earlier here we also made the world smaller change our way of thinking about  and future means of transportation will bring even more rapid radical change but even the difference between the speed of an ox cart in the fastest rocket is small when compared with the difference in by when they speak of the great change in speed or size prefer to speak in terms of a unit of measurement called an order of magnitude meaning ten times as much dr richard hamming research mathematician for the bell telephone laboratories in a paper presented before a meeting of the american academy for the advancement of science put it this way the computer revolution is often compare with the famous industrial revolution importance and scope industrial greatly change mans idea of themselves in the world in which he lives before getting into the main part is paper is necessary discussed briefly the idea of a change in a technology changes are often measured in units of the order of magnitude meaning roughly a factor of each of these have produced a whole new effects indeed it is said that the automobile is produced even a change in our morals computers have improved in speed by at least six orders of magnitude a million fold in order to understand the backroom illian because the following two situations first that you have only one dollar and second that you have a million dollars you can readily see that no two situations are fundamentally different effects you adopt a different view of yourself in the world in which you live along with the change of speed there's been a great increase in reliability so we now do much longer computations then with practical by hand finally with the increase in speed there has been a corresponding decrease in the cost something more than one thousand times cheaper it is as if suddenly automobiles cost two to four dollars houses twenty to sixty dollars and the changes in the computer technology are still going on and we hardly need to be reminded that we live in a world that is becoming more complicated and more crammed with information every day one description of this quantity of data on everything from the lifetime of earning records of an individual to the bea million personal records can be processed in one day this manufacturing plant is entirely computer controlled in accordance with rules for decision making stored in the machine this chemical plant for making polly i so green was designed by a computer in a recent example a computer in sixteen hours and out of sixteen thousand possible designs selected the design that most closely approached the ideal design engineers firing of the mother million dollars saturn rocket was simulated on this computer many times before the actual firing was authorized and the simulated firings which helped eliminate many of the problems in the functioning of the rocket cost achieved through the manipulation of numbers according to instructions given to the computer by the programmer but what are these rules what is the relationship between numbers and the real things they are said to represent these are some of the questions that we put to the scientist we've already seen dr richard hemming research mathematician but the bill telephone laboratories so i would say this present at the belt of all the aborigines we do about ten percent of experiments are computer and about ninety percent of laptops are expected in time we will do ninety percent on the computers and ten percent of the lab speed cost effort favor the computer over the laboratory approach is possible because we construct a mathematical model rather than a material much i use a work constructing as a mathematical equations a construction rather than a materialistic physical part is perhaps fortunate we have found particular field of physical sciences that are predictions based upon the mathematical models agree very well with what we observe the physical world the nineteenth century physicists heinrich hertz describe the concept of a model in these words we make for ourselves internal pictures or symbols of external objects we make them of such a kind that the necessary consequences in front of the internal pictures are always pictures of the necessary consequences in nature of the objects symbolize the idea of a mathematical majlis fairly easy to understand a very simple trivial example is the number you calculate on your check stubs you combine the various numbers by addition subtraction and they correspond in a very real sense the amount of money that you have in the bank the mathematical model is the number you manipulate the amount of money you actually have in the bank the physical world first consider now  slightly more complex example this is a common experience for most of us the front end of the car dip sharply when we come to a sudden stop in technical language there is a transfer o weight from rear to front in the action loop breaking the mathematical model of the transfer of weight can reveal exactly how much weight is on both wheels and different road surfaces and braking conditions will result in different weight distributions but the mathematical models for the transfer of weight from rear to front will remain the same in this mathematical model of behavior i will deal we can use a computer to simulate what would happen in actual fact we have actually found a mathematical models of all of your traffic predict very well many of the effects which we observe returning to our more general remarks about the use of computers we first use computers to simulate situations  engineering situation which we had been doing before by hand computers allowed us to do much larger and more complex problems but this ignored the part of magnitude effect which we spoke of we are now  one of the characteristics of human beings is that among other things that they do that they start problems and what it means of course to solve a problem is the able to not only get an answer to a question that arises in a particular situation but then to find other cases that are similar to the initial one so that we are in effect in a position to solve  or some rules then it's not entirely evident that one should be thinking of the significance of every step that one is performing but it also possible to construct the machines t in following a set of rules or programs so that in a very short span of time they're get entirely new answers they don't answer all the all questions but because the questions are new the answers are also the new and very exciting there is a strong tendency to speak of the machine solving the problem when in fact really it the program which describes to the machine what the machines do this is overlooked i think a great deal of confusion arises from this is not that we do not have adequate machines to solve our problems many times or rather we lack adequate descriptions of how to solve the problem and this is a pretty important point to understand as we spread out and learn more and more about our techniques of solving problems we will be able to do wiring wiring class a problem is not the machine so much as it is our lack of ideas controls