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ERROR CORRECTING CODES 87mention it again and again. The more elaborate the equipment is, and we are obviously going in thatdirection, the more field maintenance is vital, and error correcting codes not only mean in the field theequipment will give (probably) the right answers, but it can be maintained successfully by low levelexperts.The use of error detecting and error correcting codes is rising steadily in our society. In sending messagesfrom the space vehicles we sent to the outer planets, we often have a mere 20 watts or less of power(possibly as low as 5 watts), and had to use codes which corrected hundreds of errors in a single block ofmessage—the correction being done here on earth, of course. When you are not prepared to overcome thenoise, as in the above situation, or in cases of “deliberate jamming”, then such codes are the only knownanswer to the situation.In the late summer of 1961 I was driving across the country from my sabbatical at Stanford, Cal. to BellTelephone Laboratories in NJ and I made an appointment to stop at Morris, Illinois where the telephonecompany was installing the first electronic central office which was not an experimental one. I knew it usedHamming codes extensively, and I was, of course, welcomed. They told me they had never had a fieldinstallation go in so easily as this one did. I said to myself, “Of course, that is what I have been preaching forthe past 10 years”. When, during initial installation, any unit is set up and running properly (and you sort ofknow it is because of the self-checking and correcting properties), and you then turned your back on it toget the next part going, if the one you were neglecting developed a flaw, it told you so! The ease of initialinstallation, as well as later maintenance, was being verified right before their eyes! I cannot say too loudly,error correction not only gets the right answer when running, it can by proper design also contributesignificantly to field installation and field maintenance; and the more elaborate the equipment the moreessential these two things are.I now want to turn to the other part of the chapter. I have carefully told you a good deal of what I faced ateach stage in discovering the error correcting codes, and what I did. I did it for two reasons. First, I wantedto be honest with you and show you how easy, if you will follow Pasteur’s rule, “Luck favors the preparedmind.”, to succeed by merely preparing yourself to succeed. Yes, there were elements of luck in thediscovery; but there were many other people in much the same situation, and they did not do it! Why me?Luck, to be sure, but also I was preparing myself by trying to understand what was going on—more than theother people around who were merely reacting to things as they happened, and not thinking deeply as towhat was behind the surface phenomena.I now challenge you. What I wrote in a few pages was done in the course of a total of about three to sixmonths, mainly working at odd moments while carrying on my main duties to the company. (Patent rightsdelayed the publication for more than a year.) Does anyone dare to say they, in my position, could not havedone it? Yes, you are just as capable as I was to have done it—if you had been there and you had preparedyourself as well!Of course as you go through life you do not know what you are preparing yourself for—only you want todo significant things and not spend the whole of your life being a “janitor of science” or whatever yourprofession is. Of course luck plays a prominent role. But so far as I can see, life presents you with many,many opportunities for doing great things (define them as you will) and the prepared person usually hits oneor more successes, and the unprepared person will miss almost every time.The above opinion is not based on this one experience, or merely on my own experiences, it is the resultof studying the lives of many great scientists. I wanted to be a scientist hence I studied them, and I lookedinto discoveries which happened where I was and asked questions of those who did them. This opinion isalso based on common sense. You establish in yourself the style of doing great things, and then when
88 CHAPTER 12opportunity comes you almost automatically respond with greatness in your actions. You have trainedyourself to think and act in the proper ways.There is one nasty thing to be mentioned, however, what it takes to be great in one age is not what is requiredin the next one. Thus you, in preparing yourself for future greatness (and the possibility of greatness is morecommon and easy to achieve than you think, since it is not common to recognize greatness when it happensunder one’s nose) you have to think of the nature of the future you will live in. The past is a partial guide,and about the only one you have besides history is the constant use of your own imagination. Again, arandom walk of random decisions will not get you anywhere near as far as those taken with your own visionof what your future should be.I have both told and shown you how to be great; now you have no excuse for not doing so!
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The Art of Doing Science and Engine
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This edition published in the Taylo
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23 Mathematics 16324 Quantum Mechan
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The year 2020 seems a convenient da
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1OrientationThe purpose of this cou
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ORIENTATION 3Telephone Laboratories
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they arise so you will not be left
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ORIENTATION 7One of the main tasks
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2Foundations of the Digital (Discre
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FOUNDATIONS OF THE DIGITAL (DISCRET
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3History of Computers— HarwareThe
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HISTORY OF COMPUTERS—HARDWARE 19b
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HISTORY OF COMPUTERS—HARDWARE 21T
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HISTORY OF COMPUTERS—HARDWARE 23B
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HISTORY OF COMPUTERS—SOFTWARE 25(
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HISTORY OF COMPUTERS—SOFTWARE 27A
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HISTORY OF COMPUTERS—SOFTWARE 29F
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HISTORY OF COMPUTERS—SOFTWARE 31b
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5History of Computer ApplicationAs
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HISTORY OF COMPUTER APPLICATIONS 35
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Page 48 and 49: HISTORY OF COMPUTER APPLICATIONS 39
Page 50 and 51: asic understanding of when the meth
Page 52 and 53: ARTIFICIAL INTELLIGENCE—I 43chang
Page 54 and 55: ARTIFICIAL INTELLIGENCE—I 45Early
Page 56 and 57: 7Artificial Intelligence—IIIn thi
Page 58 and 59: ARTIFICIAL INTELLIGENCE—II 49mome
Page 60 and 61: ARTIFICIAL INTELLIGENCE—II 51have
Page 62 and 63: ARTIFICIAL INTELLIGENCE—II 53can
Page 64 and 65: 8Artificial Intelligenc—IIII sugg
Page 66 and 67: 9n-Dimensional spaceWhen I became a
Page 68 and 69: N-DIMENSIONAL SPACE 59Figure 9. IIl
Page 70 and 71: N-DIMENSIONAL SPACE 61and hence the
Page 72 and 73: N-DIMENSIONAL SPACE 63where X and Y
Page 74 and 75: N-DIMENSIONAL SPACE 653. D(x,y)=D(y
Page 76 and 77: 10Coding Theory—IHaving looked at
Page 78 and 79: CODING THEORY—I 69is uniquely dec
Page 80 and 81: CODING THEORY—I 71Figure 10.IVFig
Page 82 and 83: CODING THEORY—I 73I feel it neces
Page 84 and 85: CODING THEORY—II 75Figure 11.IFig
Page 86 and 87: CODING THEORY—II 77Figure 11.VThi
Page 88 and 89: CODING THEORY—II 79in this scheme
Page 90 and 91: 12Error Correcting CodesThere are t
Page 92 and 93: ERROR CORRECTING CODES 83Figure 12.
Page 94 and 95: ERROR CORRECTING CODES 85old syndro
Page 98 and 99: 13Information TheoryInformation The
Page 100 and 101: INFORMATION THEORY 91Figure 13.IThi
Page 102 and 103: INFORMATION THEORY 93Figure 13.IIIc
Page 104 and 105: INFORMATION THEORY 95Let us critiqu
Page 106 and 107: 14Digital Filters—INow that we ha
Page 108 and 109: DIGITAL FILTERS—I 99for any other
Page 110 and 111: DIGITAL FILTERS—I 101Figure 14.IT
Page 112 and 113: DIGITAL FILTERS—I 103Figure 14.II
Page 114 and 115: DIGITAL FILTERS—I 105Figure 14.IV
Page 116 and 117: 15Digital Filters— IIWhen digital
Page 118 and 119: DIGITAL FILTERS—II 109Let us run
Page 120 and 121: DIGITAL FILTERS—II 111Figure 15.I
Page 122 and 123: DIGITAL FILTERS—II 113At x=0 this
Page 124 and 125: 16Digital Filters—IIIWe are now r
Page 126 and 127: DIGITAL FILTERS—III 117Figure 16.
Page 128 and 129: DIGITAL FILTERS—III 119We next tu
Page 130 and 131: DIGITAL FILTERS—III 121Figure 16.
Page 132 and 133: 17Digital Filters—IVWe now turn t
Page 134 and 135: DIGITAL FILTERS—IV 125These recur
Page 136 and 137: DIGITAL FILTERS—IV 127Figure 17.I
Page 138 and 139: SIMULATION—I 129Figure 18.IThe fi
Page 140 and 141: SIMULATION—I 131(though they had
Page 142 and 143: SIMULATION—I 133Figure 18.IIIinte
Page 144 and 145: 19Simulation—IIWe now take up the
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SIMULATION—II 137The major part o
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SIMULATION—II 139energy or angula
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20Simulation—IIII will continue t
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SIMULATION—III 143Figure 20.IVFig
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SIMULATION—III 145Figure 20.VIdow
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SIMULATION—III 147Figure 20.VIIIW
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SIMULATION—III 149Now to the next
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21Fiber OpticsOne of the reasons fo
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FIBER OPTICS 153Figure 21.IIII did
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FIBER OPTICS 155Figure 21.IVFigure
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22Computer Aided Instruction—CAIB
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COMPUTER AIDED INSTRUCTION—CAI 15
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and they all knew immediately it wa
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23MathematicsAs you live your life
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MATHEMATICS 165Figure 23.IFigure 23
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MATHEMATICS 167illustrates my attit
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MATHEMATICS 169can use the same for
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24Quantum MechanicsMost physicists
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taught QM, no one has found a widel
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QUANTUM MECHANICS 175I do not prete
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CREATIVITY 177I hope the above has
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CREATIVITY 179“memorizing the mat
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26ExpertsAs remarked in an earlier
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EXPERTS 183Figure 26.ILaboratories
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EXPERTS 185Figure 26.IIthe final an
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27Unreliable DataIt has been my exp
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UNRELIABLE DATA 189But how about ba
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UNRELIABLE DATA 191country might ge
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UNRELIABLE DATA 193collection of qu
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28Systems EngineeringParables are o
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SYSTEMS ENGINEERING 197Cramming is
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of traffic performance degrades imm
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SYSTEMS ENGINEERING 201of the natur
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YOU GET WHAT YOU MEASURE 203Figure
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YOU GET WHAT YOU MEASURE 205still o
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YOU GET WHAT YOU MEASURE 207whole o
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30You and Your ResearchI have given
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YOU AND YOUR RESEARCH 211Confidence
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YOU AND YOUR RESEARCH 213know where
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YOU AND YOUR RESEARCH 215believe, i
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INDEX 217Godel’s theorem, 280grow
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