Computer and the Mind of Man : Universe of Numbers (1962)

oh [Music] from man's earliest Beginnings to the present he has been making and using tools as a means of gaining a more effective control over his environment these tools in the service of man can be divided into two groups there are tools that increase man's control through extending his physical powers and there are tools that increase his control through providing him with new information and new ways of processing this information this second group of tools consists of machines that literally enlarge our intelligence through their power to manipulate the symbols of arithmetic and logic in relation to real life situation [Music] [Music] [Music] numbers can be used to represent everything from one orange to one Galaxy models of real life situations and things can be constructed of numbers and these mathematical models can be manipulated so that we may extend our knowledge of how to control design and predict the behavior of things and processes in the real world within the past two decades the digital or number computer has made possible a major advance in our ability to store process and interpret the information that man can symbolize within the universe of numbers today computer technology is being taught even in some high schools here Fred grunberger of the Rand Corporation talks with research mathematician Richard Heming of the Bell telephone laboratory now I'd like to show you some of the things that I've been doing just as an example in training young people in Computing technology we'll bring in some instructions from the paper tape over there to do a few problems mhm at this time we're reading instructions into the storage unit of the machine which is in here and when the tape stops reading the machine is not calculating and some numbers appear now you'll notice we haven't labeled the routine because in demonstrating to high school children particularly I like to let them tell me what's going on you like to guess well that's easy that's powers of two okay they're labeled the ath power of two just came out 256 it's gone up by once now a student can readily detect that this is virtually a trivial problem in fact he can do this much arithmetic in his head as the machine is running can probably run this far now the numbers are beginning to get big now if we move a switch here we've stopped going ahead by ones and we're going ahead now by 10 the numbers are getting big very fast right this he might have a little trouble doing with pencil and paper let's move another switch we've just generated the 60th power of two now the hundred's power of two mhm notice alata it takes a little bit more time the computer is counting for us bypassing the intermediate numbers the 200's Power of Two And at the flick of another switch we'll go a little faster yet not only are we illustrating that the computer can do a little bit more this is still a very simple problem but can handle extremely large numbers here is a beehive but where are the bees hidden away where nobody sees they when I'll come creeping out of the hive 1 2 3 4 five very early in life we begin to learn numbers it usually begins with counting the fingers in fact if humans had only four fingers on each hand we would probably have a number system based on eight rather than 10 2 three four five 6 7 8 9 10 all right your round round [Applause] all right ladies and gentlemen once more the lucky wheel spin relax here it comes number everybody else loses I'll tell you one our use of numbers can be playful and serious simple and complex but the perennial problem that confronts most human beings is that we're not very good at numbers and arithmetic and so very early thousands of years before our modern era man began to invent mechanical aids for counting one of the earliest of such AIDS is the Abus a counting instrument still used in many parts of the world today like so many inventions counting machines have Arisen in response to particular needs the 17th century philosopher and mathematician BL Pascal invented an arithmetic machine to help with the boring repetitive job of making accurate calculations in his father's tax office this was the first truly mechanical calculator and it used a basic idea of arithmetic that had been missing in all previous mechanical adding machines the 10 carry idea mechanically the carrying operation means that when the unit's wheel has advanced 10 steps the 10's wheel advances one step this principle is used for example in the mileage counter of your automobile 32 years after the Pascal machine another philosopher mathematician gotfried vilhelm Fon liit invented a machine that would multiply and divide mechanically however the livits machine was not very reliable and more than two centuries were to pass before a genuinely practical and reliable calculating machine was invented for example in 1889 Leon ble invented a practical mechanical multiplier ble was only 18 at the time however the machine was never produced commercially because ble devoted the rest of his life to racing automobiles today the mechanical calculator is a familiar fixture on many an office desk but it is a limited device simply because it is mechanical that is Parts within the machine must move for every operation performed and the operator must key in every step that the machine performed this obviously takes time if a machine could carry out calculations automatically remember intermediate results and print out the final results the whole process would be speeded up considerably just such a machine was designed but not built by an English mathematician Charles babage in the 1820s financial difficulties forced babage to abandon construction of his Difference Engine a machine designed to calculate mathematical tables but his Design Incorporated automatic calculation or sequence control a mechanical means of remembering intermediate results and a means of producing results in printed form rather than requiring them to be recorded manually babbage's designs were many years ahead of the technology of his time only years later was an actual Difference Engine constructed a particular need is so often the stimulus for an invention answering that need but there must also be a technology adequate to the invention a combination of these circumstances at the beginning of this Century produced the now familiar punched card method of data input the United States census of 1880 required 7 years to complete given the rapid population growth in the United States if all the data had to be hand fed to calculating machines the 1890 census might not have been completed before time for the 1900 census a Census Bureau statistician Herman hollz observing this problem solved it by developing machines which added up the data from holes punched in pieces of cardboard the size of the then current dollar bills the Hollerith punch card Innovation permitted the 1890 senses to be completed in 3 years automatic calculation plus the punch card method of feeding in data represented a considerable increase in speed but this was still mechanical or at best an electr mechanical system made up of many moving parts and every instruction had to be placed in the machine at the appropriate time by an operator two further developments in concept and technology changed this and introduced an increase in speed and reliability that almost defies the imagination first the development of true electronic rather than mechanical or electr mechanical machines the first completely electronic calculator was ENC or electronic numerical integrator and computer designed and built in the mid 1940s by John Mockley and J preser eord well the eniac was built at the University of Pennsylvania we started work on it in 1943 and we finished it uh just a little under three years later it was quite large it occupied a 30X 50t room it weighed 30 tons it had over 40 panels in it and it had about over 18,000 vacuum tubes in it this would be uh enough to build 1,000 television sets today the uh the machine was uh primarily and originally built for ballistics calculations but one of the first uh important things we did with it was to prove that uh that electronic computers uh could be used to solve Nuclear Physics problems and uh we did a feasibility study of using an electronic computer to solve problems of this type which couldn't be solved any other way at that time on the ANC in uh in about two weeks during which we had maybe a a dozen hours of actual calculation we did work that would have taken a man with the that's calculator 100 years this is Jay presper eert now a vice president of the univac division's very ran Corporation well I think uh the first reaction that John and I had when we stood in the midst of these many panels and uh saw some 3,000 little pink lights flashing all around us was uh as if we and the other people have been involved in building a sort of Cathedral I mean we were we were impressed by the appearance of what we had done more than anything else was the addition of electronics to our calculators we increased our speed our Brute Force speed by a factor of at least a thousand but perhaps the greatest of advance of all was the concept of storing instructions within the machine in the same way that we stored data this is the concept due to John Von noyman now since the time of the invention of the stored program concept as we now call it we have gained many other things but they seem relatively small the introduction of mass production increases in speed reliability and lowering of the cost all of these pale into insignificance in comparison with the stored program concept itself a computer as we know it today is a device which can accept information in some form store it process it and produce answers in an acceptable read readable form with this definition of course goes the injunction if we're going to call it a computer that it must be able also to store its own instruction and process them from within the machine the idea of the stored program developed by John V noyman in the late 1940s is one of those simple beautiful and very powerful ideas if a machine can store numbers why not have it store instructions in the form of a number code the modern digital computer stores both data and instructions in number form it does this by converting all the information fed to it into a two-state or binary number system under the binary system any known number can be expressed by some combination of ones and Zer and letters and other symbols can also be expressed by ones and zeros in accordance with a pre-arranged code the two digits one and zero can be represented by the physical state of the electronic circuits in the computer that is voltage on can stand for one and voltage off off for zero in the electronic memory of a computer these digits are usually expressed by the direction of a magnetic field set up in tiny metal rings or cores threaded on wires magnetized North can mean one magnetize South can mean zero these individual digits are called bits a term coined from binary digit a combination of bits makes up a computer word and the size of a computer's memory is determined by the size and number of words it can store the data or numbers and the instructions in number form according to a specific code are identified in a computer memory by means of their electronic locations or addresses a computer will go from address to address in strict sequential order unless instructed to jump or Branch to a given address when branching is dependent upon the outcome of a particular calculation we have a form of decision-making a computer can also be instructed to move the address of an instruction in this way it is able to modify its own instructions and to operate at an even greater level of sophistication we are moving into a world where computers will do many of the things we have long associated with human problem solving tasks involving the making of complex decisions and the control of other machines and processes and our children will have to know much more about this technology than we do from teaching experiments that Fred grunberger and others have been conducting we know that younger Minds do not have the same resistance to the complex language of numbers natural to Computing machines that so many of us may have for young students there is a wonder and a delight in learning how to use a new and exciting tool for many youngsters the figures of logic and Mathematics hold no Terrors and they are able to master in a surprisingly brief time the rudiments of using a computer to solve difficult problems I find it delightful to let students consider this problem a little and perhaps um ask their teacher how it works MH now the last problem on the tape here illustrates again something else we're our problems are getting a little bit more complex as we go along can you tell me what this one does we get the numbers 345 on a line 10 5 12 13 that's um those are Pythagorean numbers right I took number three years ago there are integers which can satisfy the Pythagorean relationship let's stop it a second the last line we saw here 631 1665 with would satisfy a right triangle 632 + 16 s would equal 65 s let's just let this run a little bit more I'd like to use this last problem as an example of the thing we were talking about before before how do we get a computer to do a job like this for us mhm and remember we were talking about the the farway test of putting a problem on a computer remember the four points is the problem defined is there a way of doing it that is does a method exist will it fit the machine and is there a payoff now the problem is well defined in this case even for a high school student he has perhaps experimented with the first three or four lines of this table he's obviously run across the 345 triangle in his Geometry book and in class he's probably never seen the triplet 9160 109 right but at least he knows what the problem is therefore it's defined since we are generating them it's obvious to us now that there is a method but it wouldn't be obvious to a high school student that there is a method of getting all of them systematically the numbers involved here are small and the logic of the problem is very small let's for a moment look at a somewhat more commonplace problem than the generating of Pythagorean triplets how may a computer used by a banking firm be instructed to do accounting operation and to decide whether or not a particular account is overdrawn the mathematics of the problem is simple enough an accurate record of the amount of money in the account must be kept and the checks that are written must be charged off against the account it's a matter of record keeping addition and subtraction however a computer is a no nothing machine until it is instructed to perform the required calculations and decisions planning this sequence of steps for a computer to solve a problem is part of the job of the human programmer He will draw up the sequence of steps in a form called a flowchart a flowchart just because it must contain every step that the computer must perform can become very complicated but if we examine one small section of it we begin to see that indeed a computer does things in small steps but it can also make decisions as to which of several alternative steps it should take this is a simplified flowchart detail for that portion of the data processing operation where a check drawn on an account is posted against the master record for the account which is on Magnetic Tape the computer will make a decision by testing whether the account balance is negative or positive if the balance is negative it means that the account is already overdrawn the computer will then add one to its record of the number of times the account has been overdrawn it will then store or electronically file this new information next the compu is required is the amount of money sufficient to cover the check which is being processed the computer compares the amount of balance with the amount in the check the answer is yes if the balance is larger the computer will then deduct the amount of the check from the original balance and will print out this new information on the customer record however if there are not sufficient funds to cover the check the computer will record this information write an exception message and print out the appropriate customer record this tiny section of a flowchart represents only a very few of the many steps and decisions made at lightning speed by a computer in what is called demand deposit accounting however the detailed instructions on the flowchart cannot in their original form be communicated to the machine they must be translated into number form the only language which the machine can handle and understand and the Machine language or code is different with different machines Fred grunberger describes a portion of the coding or machine instructions for the problem on Pythagorean triplets this is a sample of the code taken from this specific problem we're taking just one little portion of the problem and showing the seven machine instructions which implemented inside the computer the language we use of course relates to this specific machine and would be different on another machine since each of these instructions is 12 digits long in this machine they are located somewhere in storage at areas that are 12 digits apart actually the 112 here refers to this digit within the machine as a matter of convenience now I'll translate them as we go the details are not too important but people are interested the question was is R odd and we used the idea that if we multip mply an odd number by five the final digit of the project product is a five otherwise it would be a zero so this says to the machine multiply the number called R which we have put somewhere else in storage not in this area of course up here at 10,05 by the number which is right in front of us here the number five multiply R by five and in remarks we say what we're doing now the next thing here is a detail of machine machine coding it doesn't seem to be part of the logic of our problem but these are things that have to be done we're going to get a rather long product we want simply to look at the last digit in this machine we have to fix it up to be a two-digit number so what this says is put a zero right next to the last digit mhm all right now we're back to the logic of our problem this says to the machine compare the two-digit number this should be at 99 98 well that's how things go um it's easy to make a mistake like that to get one digit wrong and this sort of thing would make the whole problem collapse if we went on the machine with these actual instructions now we'd be in quite serious trouble we'd get an overflow the machine would stop and so forth this should be a 99 compare the two-digit number now located at 99 with these two digits Zero The Logical question is is R even are its last two digits now zero now here we come to the feature which makes the stored program computer such a powerful tool the factor of a million you were talking about was a brute force factor in actual speed this is the factor which gives us computing power we have now the ability to Branch normally the machine will execute these instructions one after another in sequence but occasionally we want to make one of those two-way choices that we saw in the flowchart this says to the machine go to the instruction at 1084 if and the if here is a coded number meaning if the comparison we just made here came out to be equal and we've drawn it here on the code with arrows it says do not advance in a normal way to 1060 if that condition was met if it is not met do advance in the normal way now a beginning student is usually rather impressed with the tremendous amount of detail which we have to use to implement such a very simple concept these are even or odd it seems very easy and it's taking us seven instructions each of 12 digits Each of which had better be correct in every digit or we're going to be in trouble just to get this one little part of the problem done and as we saw before the whole flowchart of the problem is quite long it's going to take a considerable number of instructions perhaps as many as 150 for this problem just to get this flowchart implemented in the computer [Music] code and we spoke in the language of numbers and reached understanding the nature of things is number this statement can be traced to Pythagoras and his followers in truth everything that can be known as a number for the nature of number is the cause of recognition able to give guidance and teaching to every man in what is puzzling and unknown for none of existing things would be clear to anyone either in themselves or in their relationship to one another unless there existed number and its Essence today our interest is not in any mystical value associated with number rather it is in the use of number as a means of extending our understanding and control and computers these machines that extend our intelligence of things bring the vast Universe of number within our reach in controlling what we choose to control in predicting what we seek to predict and in planning those great works of the imagination that may take us into Worlds beyond our own Roger zg and I feel fine capsule is turning around oh that view is tremendous [Music] is this is NE National educational television