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SIMULATION—I 133Figure 18.IIIinterconnected linear differential equations, each one giving the probability distribution of that many callson the central office as a function of the total load. Of course on a finite machine something must be done,and I had only 12 integrators, as I remember. I viewed it as an impedance line, and using the difference ofthe last two computed probabilities I assumed they were proportional to the difference of the next two, (Iused a reasonable constant of proportionality derived from the difference from the two earlier functions) thusthe term from the next equation beyond what I was computing was reasonably supplied. The answers werequite popular with the switching department, and made an impression, I believe, on my boss who still had alow opinion of computing machines.There were underwater simulations, especially of an acoustic array put down in the Bahamas by a friendof mine where, of course, in winter he often had to go to inspect things and take further measurements.There were numerous simulations of transistor design and behavior. There were simulations of the microwave “jump-jump” relay stations with their receiver horns, and the overall stability arising from a singleblip at one end going through all the separate relay stations. It is perfectly possible while each stationrecovers promptly from the blip, never-the-less the size of the blip could grow as it crossed the continent.At each relay station there was stability in the sense the pulse died out in time, but there was also thequestion of the stability in space—did a random pulse grow indefinitely as it crossed the continent? Forcolorful reasons I named the problem “Space stabilization”. We had to know the circumstances in whichthis could and could not happen—hence a simulation was necessary because, among other things, the shapeof the blip changed as it went across the continent.I hope you see almost any situation you can describe by some sort of mathematical description can besimulated in principle. In practice you have to be very careful when simulating an unstable situations—though I will tell you in Chapter 20 about an extreme case I had to solve because it was important to theLaboratories, and that meant, at least to me, I had to get the solution, no matter what excuses I gave myselfit could not be done. There are always answers of some sort f or important problems if you are determinedto get them. They may not be perfect, but in desperation something is better than nothing—provided it isreliable!Faulty simulations have caused people to abandon good ideas, and these occur all too often! However, oneseldom sees them in the literature as they are very, very seldom reported. One famuous faulty simulationwhich was widely reported (before the errors were noted by others) was a whole world simulation done bythe so called “Club of Rome”. It turned out the equations they chose were designed to show a catastrophy
134 CHAPTER 18no matter how you started or chose most of the coefficients! But it also turned out when others finally gotthe equations and tried to repeat the computations the comuputations has serious errors! I will turn to thisaspect of simulating things in the next chapter as it is a very serious matter— to either report things whichmake people believe what they want to believe, and are not so, or which you discourage people frompursuing their good ideas.
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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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asic understanding of when the meth
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ARTIFICIAL INTELLIGENCE—I 43chang
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ARTIFICIAL INTELLIGENCE—I 45Early
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7Artificial Intelligence—IIIn thi
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ARTIFICIAL INTELLIGENCE—II 49mome
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ARTIFICIAL INTELLIGENCE—II 51have
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ARTIFICIAL INTELLIGENCE—II 53can
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8Artificial Intelligenc—IIII sugg
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9n-Dimensional spaceWhen I became a
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N-DIMENSIONAL SPACE 59Figure 9. IIl
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N-DIMENSIONAL SPACE 61and hence the
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N-DIMENSIONAL SPACE 63where X and Y
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N-DIMENSIONAL SPACE 653. D(x,y)=D(y
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10Coding Theory—IHaving looked at
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CODING THEORY—I 69is uniquely dec
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CODING THEORY—I 71Figure 10.IVFig
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CODING THEORY—I 73I feel it neces
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CODING THEORY—II 75Figure 11.IFig
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CODING THEORY—II 77Figure 11.VThi
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CODING THEORY—II 79in this scheme
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12Error Correcting CodesThere are t
Page 92 and 93: ERROR CORRECTING CODES 83Figure 12.
Page 94 and 95: ERROR CORRECTING CODES 85old syndro
Page 96 and 97: ERROR CORRECTING CODES 87mention it
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 144 and 145: 19Simulation—IIWe now take up the
Page 146 and 147: SIMULATION—II 137The major part o
Page 148 and 149: SIMULATION—II 139energy or angula
Page 150 and 151: 20Simulation—IIII will continue t
Page 152 and 153: SIMULATION—III 143Figure 20.IVFig
Page 154 and 155: SIMULATION—III 145Figure 20.VIdow
Page 156 and 157: SIMULATION—III 147Figure 20.VIIIW
Page 158 and 159: SIMULATION—III 149Now to the next
Page 160 and 161: 21Fiber OpticsOne of the reasons fo
Page 162 and 163: FIBER OPTICS 153Figure 21.IIII did
Page 164 and 165: FIBER OPTICS 155Figure 21.IVFigure
Page 166 and 167: 22Computer Aided Instruction—CAIB
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Page 170 and 171: and they all knew immediately it wa
Page 172 and 173: 23MathematicsAs you live your life
Page 174 and 175: MATHEMATICS 165Figure 23.IFigure 23
Page 176 and 177: MATHEMATICS 167illustrates my attit
Page 178 and 179: MATHEMATICS 169can use the same for
Page 180 and 181: 24Quantum MechanicsMost physicists
Page 182 and 183: taught QM, no one has found a widel
Page 184 and 185: QUANTUM MECHANICS 175I do not prete
Page 186 and 187: CREATIVITY 177I hope the above has
Page 188 and 189: CREATIVITY 179“memorizing the mat
Page 190 and 191: 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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