1 00:00:13,814 --> 00:00:16,531 Thank you very much, absolute pleasure to be here. 2 00:00:16,531 --> 00:00:18,361 We all know why we're here. 3 00:00:18,361 --> 00:00:22,689 We're here to celebrate the 200th anniversary of the birth of Ada Lovelace. 4 00:00:22,689 --> 00:00:26,264 And in 1843, Ada Lovelace published a paper called Sketch 5 00:00:26,264 --> 00:00:30,919 of the Analytical Engine, which described a vast mechanical calculating engine 6 00:00:30,919 --> 00:00:36,881 designed by the mathematician and lifelong friend of Ada, called Charles Babbage. 7 00:00:36,881 --> 00:00:41,817 And any claim to fame that Ada has, as a pioneer in the history of computing 8 00:00:41,817 --> 00:00:48,041 is based on the contents of this particular paper, this sketch. 9 00:00:48,041 --> 00:00:49,561 It was her only substantial publication, 10 00:00:49,561 --> 00:00:54,561 she died 9 years later in 1852 at the age of 36. 11 00:00:54,561 --> 00:00:57,241 So, everything we wish to say, and 12 00:00:57,241 --> 00:01:00,031 that is not about the huge variety of other interests. 13 00:01:00,031 --> 00:01:04,771 Everything we would need to say about her as having a role or a place in the history 14 00:01:04,771 --> 00:01:08,691 of computing is based on this specific and single publication. 15 00:01:08,691 --> 00:01:14,531 And that's what we will be hearing a great deal about in some of the coming sessions. 16 00:01:14,531 --> 00:01:17,631 So what I propose to do is something very specific. 17 00:01:17,631 --> 00:01:21,191 What I propose to do is tell you enough about the analytical engine for 18 00:01:21,191 --> 00:01:27,211 us to make a judgement about the nature and the value of what Lovelace did. 19 00:01:27,211 --> 00:01:28,321 So it's quite narrow. 20 00:01:28,321 --> 00:01:31,211 I will not be dealing with whether Lovelace's 21 00:01:31,211 --> 00:01:34,041 relationship to drugs was entirely medicinal. 22 00:01:34,041 --> 00:01:37,965 I will not be dealing with whether her gambling addiction was an altruistic 23 00:01:37,965 --> 00:01:42,137 attempt to restore the family fortunes by recovering some of the huge amounts of 24 00:01:42,137 --> 00:01:45,376 money her husband William King had expended on his bizarre and 25 00:01:45,376 --> 00:01:46,768 vast building projects. 26 00:01:46,768 --> 00:01:51,389 >> Might want to put in the slide to show. 27 00:01:51,389 --> 00:01:56,707 >> [LAUGH] >> Not yet. 28 00:01:56,707 --> 00:02:01,246 >> [LAUGH] >> [INAUDIBLE] 29 00:02:01,246 --> 00:02:03,849 >> [SOUND] 30 00:02:03,849 --> 00:02:05,932 Oh. 31 00:02:05,932 --> 00:02:07,604 We need to go back to the beginning. 32 00:02:07,604 --> 00:02:09,449 That's it. 33 00:02:09,449 --> 00:02:19,225 >> Do you want [INAUDIBLE] 34 00:02:19,225 --> 00:02:21,501 >> The title slide before that is the one we need. 35 00:02:21,501 --> 00:02:25,923 >> Yeah, it's [INAUDIBLE]. 36 00:02:25,923 --> 00:02:26,481 >> That's it. 37 00:02:26,481 --> 00:02:30,451 >> Okay, well when you need it, just go into, click the next one in there. 38 00:02:30,451 --> 00:02:32,761 >> I'll use this. 39 00:02:32,761 --> 00:02:34,257 >> When do you want the next slide? 40 00:02:34,257 --> 00:02:39,689 [CROSSTALK] 41 00:02:39,689 --> 00:02:42,894 >> [APPLAUSE] 42 00:02:42,894 --> 00:02:45,046 >> So, some of the things i will not be 43 00:02:45,046 --> 00:02:49,724 dealing with in my narrow compass of dealing with only analytical engine, 44 00:02:49,724 --> 00:02:55,081 is the various things that have stories, narratives, that by her. 45 00:02:55,081 --> 00:02:59,061 And related drugs, the questions whether her attempts to gamble were actually 46 00:02:59,061 --> 00:03:02,571 quite altruistic to restore the family fortunes, to recover monies that her 47 00:03:02,571 --> 00:03:10,281 husband expended on these vast building, construction projects on his many estates. 48 00:03:10,281 --> 00:03:16,101 Whether her mother Anna Milbanke was an enlightened educationalist or 49 00:03:16,101 --> 00:03:21,141 whether she was in fact a vindictive disciplinarian. 50 00:03:21,141 --> 00:03:24,571 And finally the construction of her reputation in the modern age. 51 00:03:24,571 --> 00:03:27,991 There's a feast of papers to follow that's gonna address these many dimensions of 52 00:03:27,991 --> 00:03:29,241 Lovelace's life. 53 00:03:29,241 --> 00:03:32,761 So what I'm concerned specifically with here this morning is, 54 00:03:32,761 --> 00:03:37,991 what was it about Babbage's machine that so seized Lovelace's imagination? 55 00:03:37,991 --> 00:03:40,741 And what was it that she said about it that was supposedly so remarkable. 56 00:03:40,741 --> 00:03:46,320 So, it's quite a narrow compass. 57 00:03:46,320 --> 00:03:51,161 And now. 58 00:03:51,161 --> 00:03:55,927 Babbage met Lovelace in June 1833 as a society due. 59 00:03:55,927 --> 00:04:01,161 [COUGH] This image on the left is taken 60 00:04:01,161 --> 00:04:05,981 from a portrait that was done for her coming out party. 61 00:04:05,981 --> 00:04:09,851 As a member of the aristocracy, she was entitled to be represented in court and 62 00:04:09,851 --> 00:04:12,091 that which was on the 10th of May. 63 00:04:12,091 --> 00:04:15,711 And this dates within three weeks of her meeting Babbage, 64 00:04:15,711 --> 00:04:17,201 Babbage is slightly older. 65 00:04:17,201 --> 00:04:22,181 Lovelace was 17, Babbage was 42 at this particular meeting. 66 00:04:22,181 --> 00:04:26,323 And Lady Byron wrote that Ada was delighted with Babbage, 67 00:04:26,323 --> 00:04:29,191 she was full of animation and talked about his wonderful machine. 68 00:04:29,191 --> 00:04:34,551 12 days later that's on the 17th day of June, 69 00:04:34,551 --> 00:04:40,771 Lady Byron and Ada Byron visited Babbage at his house in Dawson Street and 70 00:04:40,771 --> 00:04:43,361 had a demonstration of what was built of his first difference engine. 71 00:04:43,361 --> 00:04:48,374 And this was Lovelace's first exposure to both to Babbage, 72 00:04:48,374 --> 00:04:54,125 and his concept of his engines. 73 00:04:54,125 --> 00:04:55,025 At the time they met, 74 00:04:55,025 --> 00:04:58,038 Babbage was a prominent and controversial figure in scientific life. 75 00:04:58,038 --> 00:05:05,001 He was well known for several mathematical publications, 13 in fact before he was 30. 76 00:05:05,001 --> 00:05:08,216 He was ambivalently famous for the invention of his machine which he failed 77 00:05:08,216 --> 00:05:11,091 to build at massive government expense. 78 00:05:11,091 --> 00:05:15,881 He was capable of great charm, and also of brazen rudeness. 79 00:05:15,881 --> 00:05:19,661 He felt somehow that being right entitled him to be rude. 80 00:05:19,661 --> 00:05:20,871 He was fiercely principled. 81 00:05:20,871 --> 00:05:24,711 His enemies could do no right and his friends could do no wrong. 82 00:05:24,711 --> 00:05:28,381 He was capable of [COUGH] excuse me, 83 00:05:28,381 --> 00:05:32,441 incontinent savagery in his attacks on the scientific establishment 84 00:05:32,441 --> 00:05:36,301 about what he alleged to be their poor superintendence of science. 85 00:05:36,301 --> 00:05:41,601 He was in fact the enfant terrible of science well into adulthood. 86 00:05:41,601 --> 00:05:44,111 So we have a complex and imposing figure. 87 00:05:44,111 --> 00:05:48,331 Ada was keen to meet him, she was keen to make her mark in the world of ideas and 88 00:05:48,331 --> 00:05:51,981 to be exposed to cultural and intellectual protagonists, and 89 00:05:51,981 --> 00:05:57,351 Babbage was certainly a big figure and encouraged by her mother to meet. 90 00:05:57,351 --> 00:06:00,150 So the question is, back to our narrow program, 91 00:06:00,150 --> 00:06:04,317 what was it that Lovelace saw on that day in which Babbage demonstrated, 92 00:06:04,317 --> 00:06:11,937 amongst other things, his theory of miracles? 93 00:06:11,937 --> 00:06:12,962 What does the engine do? 94 00:06:12,962 --> 00:06:15,656 How does it work and how did it come to be? 95 00:06:15,656 --> 00:06:18,748 Now we're going to spend a bit of time in 96 00:06:18,748 --> 00:06:23,250 engine one because central ideas about the core ideas in computing. 97 00:06:23,250 --> 00:06:26,460 Recognizable in modern computing were actually developed as a result of Baggage's 98 00:06:26,460 --> 00:06:28,661 speculations on differences engine one. 99 00:06:28,661 --> 00:06:32,801 In virtue of being an automaton, in virtue of it being automatic. 100 00:06:32,801 --> 00:06:34,831 And we will spend briefly some time on this. 101 00:06:34,831 --> 00:06:37,321 It also helps to understand what is 102 00:06:37,321 --> 00:06:39,771 involved in the implementation of mechanical logic, 103 00:06:39,771 --> 00:06:43,501 of which there's several examples outside by projects that are ongoing now to see 104 00:06:43,501 --> 00:06:48,331 how else might Babbage have done that, had he not done it in the way he did. 105 00:06:48,331 --> 00:06:51,171 So, how did it all come to be? 106 00:06:51,171 --> 00:06:53,301 What were Babbage's aspirations, what were his expectations, 107 00:06:53,301 --> 00:06:55,631 why was he doing this at all? 108 00:06:55,631 --> 00:07:00,901 The genesis episode is captured in a well-known vignette of Spring 1821, 109 00:07:00,901 --> 00:07:05,451 Babbage and Herschel are sitting and checking 110 00:07:05,451 --> 00:07:09,481 the accuracy of mathematical astronomical tables that have been calculated by hand. 111 00:07:09,481 --> 00:07:11,721 Increasingly errors become evident. 112 00:07:11,721 --> 00:07:15,341 Babbage becomes increasingly agitated by these errors and he, as it were, 113 00:07:15,341 --> 00:07:17,181 clasps his hands to his head and says, 114 00:07:17,181 --> 00:07:21,791 I wish to God these calculations had been executed by steam. 115 00:07:21,791 --> 00:07:23,311 Steam being a metaphor both for 116 00:07:23,311 --> 00:07:28,301 the infallibility of machinery and as a metaphor for industrial production. 117 00:07:28,301 --> 00:07:31,776 The idea is that machines would be a factory of numbers and 118 00:07:31,776 --> 00:07:35,401 his son actually says, the machine be a manufactory of numbers. 119 00:07:35,401 --> 00:07:38,241 So we have number as industrial product. 120 00:07:38,241 --> 00:07:44,013 It's the extension of the industrial metaphor from the production of goods, 121 00:07:44,013 --> 00:07:47,687 the production of if you like, mental products, 122 00:07:47,687 --> 00:07:53,124 the transition from matter to mind, from thing to thought, if you like. 123 00:07:53,124 --> 00:07:54,721 So that's the genesis episode. 124 00:07:54,721 --> 00:07:57,671 So Babbage became completely enraptured in this idea, 125 00:07:57,671 --> 00:08:01,161 became ill with the intensity with which he works, and he immediately sat down and 126 00:08:01,161 --> 00:08:03,401 started devising how he might do this. 127 00:08:03,401 --> 00:08:07,481 And rushed down to Hershel, in Slough, a few weeks later, with some manuscripts, 128 00:08:07,481 --> 00:08:10,741 which we're going to see for the first time today. 129 00:08:10,741 --> 00:08:13,921 So the engine that Babbage first designed was difference engine number one, so 130 00:08:13,921 --> 00:08:16,673 called because of the mathematical principle on which it's based, 131 00:08:16,673 --> 00:08:21,141 which is the mass of the finite differences. 132 00:08:21,141 --> 00:08:25,841 This is the piece that Lovelace saw, it is one-seventh of the full-size engine. 133 00:08:25,841 --> 00:08:28,631 It is full scale, but it is one-seventh of the full engine. 134 00:08:28,631 --> 00:08:30,951 And that's all that was built in Babbage's lifetime. 135 00:08:30,951 --> 00:08:34,361 In fact, it's the most substantial artifact of a half a century of effort, 136 00:08:34,361 --> 00:08:39,921 of design and development effort, that Babbage undertook. 137 00:08:39,921 --> 00:08:41,781 So how does it work? 138 00:08:41,781 --> 00:08:46,081 Well, number values are represented by the rotation, the angular rotation, 139 00:08:46,081 --> 00:08:46,651 of figure wheels. 140 00:08:46,651 --> 00:08:49,541 So we can see that these columns of figure wheels, number wheels, 141 00:08:49,541 --> 00:08:52,441 are represented by the angular rotation. 142 00:08:52,441 --> 00:08:55,331 A multi-digit number is represented by a column of wheels, 143 00:08:55,331 --> 00:08:56,731 that we can see on the right here. 144 00:08:56,731 --> 00:08:59,331 With units at the bottom, tens above, hundreds, and so on. 145 00:08:59,331 --> 00:09:03,181 So if you wanted to represent 2.5 you do not take a wheel and 146 00:09:03,181 --> 00:09:05,321 put it between 2 and 3. 147 00:09:05,321 --> 00:09:06,731 You have a wheel which has a two on it and 148 00:09:06,731 --> 00:09:08,911 a wheel which has a three on it and they sit as a stack. 149 00:09:08,911 --> 00:09:10,241 So this is digital. 150 00:09:10,241 --> 00:09:14,131 Only whole numbers are legitimate and determinant values. 151 00:09:14,131 --> 00:09:17,271 Now we know that wheels are not digital devices. 152 00:09:17,271 --> 00:09:21,511 All the intermediate values are viable and stable. 153 00:09:21,511 --> 00:09:25,541 So, the machine would be infallible, not in virtue of being mechanical. 154 00:09:25,541 --> 00:09:29,661 It would be infallible because Babbage could make control mechanisms that would 155 00:09:29,661 --> 00:09:31,331 enforce digital operations. 156 00:09:31,331 --> 00:09:35,181 So, the idea, how he dealt with the issue of certainty was to 157 00:09:35,181 --> 00:09:38,351 ensure digital operations through the control mechanism. 158 00:09:38,351 --> 00:09:42,391 And this is what occupied a great deal of Babbage's efforts to ensure 159 00:09:42,391 --> 00:09:45,661 that the integrity of the calculation could not be compromised, and 160 00:09:45,661 --> 00:09:53,921 we're gonna look at a mechanism by which he manages to do that. 161 00:09:53,921 --> 00:09:59,291 This is a mechanism of difference engine one, and we can see there a sprung lever. 162 00:09:59,291 --> 00:10:03,361 This is a lever with a spring there, 163 00:10:03,361 --> 00:10:07,501 which biases the lever, into the space between the lobes. 164 00:10:07,501 --> 00:10:13,161 So, you can see that as this wheel turns, the sprung lever biases it so 165 00:10:13,161 --> 00:10:18,981 that it favors resting in the position that is an integral whole number. 166 00:10:18,981 --> 00:10:20,451 Now, the lever performs three functions. 167 00:10:20,451 --> 00:10:24,031 It performs error prevention, error correction and error detection. 168 00:10:24,031 --> 00:10:28,391 So, error prevention, if the wheel is slightly deranged, 169 00:10:28,391 --> 00:10:32,611 the roller will slightly, we can look at that slightly more closely. 170 00:10:32,611 --> 00:10:36,289 The roller will push in between the lobes and centre it. 171 00:10:36,289 --> 00:10:40,311 If the lever is locked, it will prevent the wheel deranging 172 00:10:40,311 --> 00:10:42,461 during periods in which it's not supposed to move. 173 00:10:42,461 --> 00:10:47,151 And if the wheel is on the cusp, the top of the lobe, 174 00:10:47,151 --> 00:10:50,511 it indicates that this wheel is in an indeterminate position, the integrity of 175 00:10:50,511 --> 00:10:53,641 the calculation is being compromised, stop the machine, jam the machine. 176 00:10:53,641 --> 00:10:56,127 So jamming is not the catastrophe you would think it is. 177 00:10:56,127 --> 00:10:59,101 Machines that were subsequent --, they are designed to jam. 178 00:10:59,101 --> 00:11:00,451 Jamming is a form of error correction. 179 00:11:00,451 --> 00:11:06,581 It's an alert that the integrity of their calculation has been compromised. 180 00:11:06,581 --> 00:11:07,601 So these are digital wheels. 181 00:11:07,601 --> 00:11:10,971 It's evident, it's clearly here that this is an attempt to digitize and 182 00:11:10,971 --> 00:11:15,731 discretize mechanical motion to ensure the integrity and accuracy of results. 183 00:11:15,731 --> 00:11:20,041 That's how I dealt with the issue of reliability. 184 00:11:20,041 --> 00:11:25,421 Now, this was not the result of a failed series of trials, going digital. 185 00:11:25,421 --> 00:11:27,981 It was evident in the very earliest conception of the machine. 186 00:11:27,981 --> 00:11:31,851 Because we have what we believe are the very first scribblings after Babbage's 187 00:11:31,851 --> 00:11:35,881 mechanical epiphany in spring 1821, where he wrote down what he might do, and 188 00:11:35,881 --> 00:11:38,611 he rushes down to Herschel to go and explain what his ideas were. 189 00:11:38,611 --> 00:11:39,451 And we belive in these, 190 00:11:39,451 --> 00:11:45,531 the manuscripts are in the Museum of the History of Science in Oxford. 191 00:11:45,531 --> 00:11:48,690 You can see immediately, this is the very earliest document, he thought Babbage 192 00:11:48,690 --> 00:11:51,785 himself thought it dated from 1820, we know it dates from early 1821. 193 00:11:51,785 --> 00:11:56,731 You can see immediately that there are lobes on these wheels. 194 00:11:56,731 --> 00:12:00,321 There's a ratchet, he talks about click wheels and ratchets. 195 00:12:00,321 --> 00:12:05,621 There's the sprung lever and if we look at the next one we can see the steel roller, 196 00:12:05,621 --> 00:12:07,481 the leaf spring, and the lobes. 197 00:12:07,481 --> 00:12:10,421 This was embedded in the very earliest conception that the machine was 198 00:12:10,421 --> 00:12:11,461 gonna be digital. 199 00:12:11,461 --> 00:12:17,571 That's how he dealt with uncertainty. 200 00:12:17,571 --> 00:12:23,294 What does the machine do? 201 00:12:23,294 --> 00:12:27,881 [COUGH] The way the machine works is you enter 202 00:12:27,881 --> 00:12:30,721 initial values that you calculate by hand onto these wheels by hand. 203 00:12:30,721 --> 00:12:35,611 You then crank the handle at the top of the top plate, which is here. 204 00:12:35,611 --> 00:12:38,311 And the machine adds a number on that column to that column to that column 205 00:12:38,311 --> 00:12:41,071 according to the method of finite difference which we needn't go into. 206 00:12:41,071 --> 00:12:45,247 But, what it allows you to do is calculate a pulse of mathematical expressions called 207 00:12:45,247 --> 00:12:49,423 polynomials by repeated edition only and eliminates the need for multiplication and 208 00:12:49,423 --> 00:12:53,091 division in which you ordinarily would be needed to do such calculations. 209 00:12:53,091 --> 00:12:54,671 So that's the value of the principle and 210 00:12:54,671 --> 00:13:01,891 what the machine does is repeated addition by cranking the handle. 211 00:13:01,891 --> 00:13:05,421 This is probably the most celebrated icon in the pre-history of computing. 212 00:13:05,421 --> 00:13:08,301 It is the first machine to successfully incorporate mathematical 213 00:13:08,301 --> 00:13:09,721 rule in mechanism. 214 00:13:09,721 --> 00:13:13,681 You crank the handle and exert physical energy, and you can get results which up 215 00:13:13,681 --> 00:13:17,851 to that point in time could only be achieved by mental effort. 216 00:13:17,851 --> 00:13:21,921 The idea that the machine was thinking was not lost on Babbage or his contemporaries. 217 00:13:21,921 --> 00:13:26,611 Lady Byron, who with Ada visited the machine, wrote in her diary, 218 00:13:26,611 --> 00:13:30,151 last week we saw the thinking machine, for such it seems. 219 00:13:30,151 --> 00:13:33,781 Harry Wilmot Buxton, a junior colleague of Babbage's wrote, the marvelous pulp and 220 00:13:33,781 --> 00:13:37,191 fiber of the brain had been replaced by brass and iron. 221 00:13:37,191 --> 00:13:41,991 He, Babbage, had taught wheelwork to think, or to do the office of thought. 222 00:13:41,991 --> 00:13:51,481 So we see the extension of the industrial metaphor for ideas of mental product. 223 00:13:51,481 --> 00:13:53,101 What were Babbage's expectations of this engine? 224 00:13:53,101 --> 00:13:55,881 What did he think they were for? 225 00:13:55,881 --> 00:13:59,701 And Babbage was 28 when he first conceived of this engine. 226 00:13:59,701 --> 00:14:03,408 And up to that point his intellectual life had been dominated entirely by 227 00:14:03,408 --> 00:14:04,207 mathematics. 228 00:14:04,207 --> 00:14:08,396 [COUGH] From school, he did the tripos at Cambridge and then came up to London. 229 00:14:08,396 --> 00:14:11,136 And by the age of 29 he had published 13 mathematical papers. 230 00:14:11,136 --> 00:14:12,954 He was a man steeped in mathematics, 231 00:14:12,954 --> 00:14:15,606 which he confessed subsequently was his first love. 232 00:14:15,606 --> 00:14:17,661 So we have a mathematician. 233 00:14:17,661 --> 00:14:23,425 For the first time with an automatic machine, a machine capable of autonomy, 234 00:14:23,425 --> 00:14:29,385 speculating what the implications and potential for machine computation was. 235 00:14:29,385 --> 00:14:33,866 And between June and December 1822, he wrote 6 papers, and 236 00:14:33,866 --> 00:14:36,891 none of them have to do with Herizon tables. 237 00:14:36,891 --> 00:14:39,414 They're all to do with mathematical potential, and 238 00:14:39,414 --> 00:14:41,158 what he writes is quite remarkable. 239 00:14:41,158 --> 00:14:43,762 What he says is the machine can solve equations. 240 00:14:43,762 --> 00:14:47,381 And I don't know if there's time but let's very briefly say how it solve equations. 241 00:14:47,381 --> 00:14:51,469 The way you solve an equation in analytic school is you equate the root of 242 00:14:51,469 --> 00:14:55,220 an equation is the value of the independent variable that reduces 243 00:14:55,220 --> 00:14:56,668 the expression to zero. 244 00:14:56,668 --> 00:14:59,823 Now if the machine is producing a result on the last-- 245 00:14:59,823 --> 00:15:01,843 the machine is producing a result on the last--. 246 00:15:01,843 --> 00:15:04,500 For example on the last computation, each time you crank the handle, 247 00:15:04,500 --> 00:15:05,998 it produces the x value of expression. 248 00:15:05,998 --> 00:15:10,138 You have found a root when the all zero state appears on the last. 249 00:15:10,138 --> 00:15:13,130 If the result is zero, then the number of times you crank the handle is the value of 250 00:15:13,130 --> 00:15:14,059 independent variable. 251 00:15:14,059 --> 00:15:19,018 So he suddenly sees the idea of computation as systematic method for 252 00:15:19,018 --> 00:15:20,237 the first time. 253 00:15:20,237 --> 00:15:22,503 And he was the first person to be in the position to actually speculate 254 00:15:22,503 --> 00:15:23,137 on these grounds. 255 00:15:23,137 --> 00:15:25,044 So, the machine can solve equations. 256 00:15:25,044 --> 00:15:26,390 It can find the value of a series for 257 00:15:26,390 --> 00:15:28,534 which there's no general expression of the. 258 00:15:28,534 --> 00:15:29,322 You crank through, 259 00:15:29,322 --> 00:15:32,484 you find the value, you don't need to know how to calculate that analytically. 260 00:15:32,484 --> 00:15:34,086 There was heuristic value. 261 00:15:34,086 --> 00:15:36,657 You could set the machine up to do various things, for 262 00:15:36,657 --> 00:15:38,672 which there was no analytic expression. 263 00:15:38,672 --> 00:15:40,874 So there were new series you could produce, 264 00:15:40,874 --> 00:15:44,756 because you had a generative rule that was mechanical, but not analytical. 265 00:15:44,756 --> 00:15:49,260 He saw that there'd be a need for a branch which we now call numeric analysis, 266 00:15:49,260 --> 00:15:53,158 of analyzing problems to optimize them for machine computation. 267 00:15:53,158 --> 00:15:56,300 So he used an example of what he writes a mathematical expression, and 268 00:15:56,300 --> 00:15:59,550 say, in that form, you need 35 multiplications in one division, and 269 00:15:59,550 --> 00:16:03,176 you can manipulate that to produce a mathematically identical expression, and 270 00:16:03,176 --> 00:16:06,992 use five multiplications and one addition, for example, as an example, he gave. 271 00:16:06,992 --> 00:16:11,115 So, you would manipulate things to optimize it for machine computation. 272 00:16:11,115 --> 00:16:14,891 And he predicts that without machine computation, science with 273 00:16:14,891 --> 00:16:18,619 through what he calls the overwhelming encumbrance of numerical detail. 274 00:16:18,619 --> 00:16:23,918 So he sees the potential reliance of science on machine computation for 275 00:16:23,918 --> 00:16:25,340 its own survival. 276 00:16:25,340 --> 00:16:30,686 So at the time Ada Lovelace comes into the scene, enters the scene in June 1833, 277 00:16:30,686 --> 00:16:34,319 Babbage had been working on his machines for 12 years. 278 00:16:34,319 --> 00:16:37,331 He was an accomplished and published mathematician, and 279 00:16:37,331 --> 00:16:40,281 he had an opportunity in his very early days, 1822, 280 00:16:40,281 --> 00:16:44,289 to speculate about the implications and potential of machine computation. 281 00:16:44,289 --> 00:16:47,136 Babbage, as we know, never completed any of his machines, but 282 00:16:47,136 --> 00:16:50,671 there is an epilogue, there is a machine that was completed to original designs 283 00:16:50,671 --> 00:16:53,331 which is difference engine number two designed 1847. 284 00:16:53,331 --> 00:16:57,039 I had the good fortune to be responsible for the construction of this machine, and 285 00:16:57,039 --> 00:16:58,828 I mentioned that there is an epilogue. 286 00:16:58,828 --> 00:17:01,464 This is a machine that weighs five tons, it has 8,000 parts. 287 00:17:01,464 --> 00:17:04,678 It works exactly as Babbage describes. 288 00:17:04,678 --> 00:17:08,199 It took 17 years to build, and it's at the Science Museum and 289 00:17:08,199 --> 00:17:10,798 can be demonstrated if anyone is interested. 290 00:17:10,798 --> 00:17:12,989 I have a four-minute video of the thing operating. 291 00:17:12,989 --> 00:17:14,957 It is quite a sumptuous spectacle to see. 292 00:17:14,957 --> 00:17:20,548 It’s a mechanical choreography, a ballet of mechanical extraordinariness. 293 00:17:20,548 --> 00:17:23,742 And since the title of this lecture is Visions of Computing, 294 00:17:23,742 --> 00:17:27,876 we're talking about a literal vision it is difficult to see how one would not, 295 00:17:27,876 --> 00:17:30,694 if one was a victorian contemplating such a machine, 296 00:17:30,694 --> 00:17:37,422 be inspired by the potential of what these machines might do. 297 00:17:37,422 --> 00:17:42,224 Babbage invented, I'm not gonna spend much time, because Adrian Johnson is gonna be 298 00:17:42,224 --> 00:17:45,142 speaking about a project which touches on all this. 299 00:17:45,142 --> 00:17:49,402 Babbage devised some symbolic language called mechanical notation, 300 00:17:49,402 --> 00:17:51,397 he was inordinately proud of it. 301 00:17:51,397 --> 00:17:54,539 It's fate was that of spectacular obscurity. 302 00:17:54,539 --> 00:17:58,489 The point is there is no comprehensive grammar book, there is no complete 303 00:17:58,489 --> 00:18:02,818 lexicon, and nobody speaks the language, and if you think of the engine as a text 304 00:18:02,818 --> 00:18:07,213 and you think of the notation as a text, which are expressions of a unifying idea, 305 00:18:07,213 --> 00:18:11,034 we can use our intimate knowledge of the engine to decode the notation, 306 00:18:11,034 --> 00:18:15,092 which is what we found out in Adrian when he's talking about that project. 307 00:18:15,092 --> 00:18:17,830 I was saying about sumptuous spectacle, that's the back of the engine. 308 00:18:17,830 --> 00:18:19,099 And this is the kind of notation. 309 00:18:19,099 --> 00:18:20,213 It looks like mathematics. 310 00:18:20,213 --> 00:18:21,258 It is not a calculus. 311 00:18:21,258 --> 00:18:22,930 It isn't scripted notation. 312 00:18:22,930 --> 00:18:26,130 And that's what we can now read as a result of having built the engine without 313 00:18:26,130 --> 00:18:27,341 reference to the notation. 314 00:18:27,341 --> 00:18:32,496 So that's just a trailer for a later presentation. 315 00:18:32,496 --> 00:18:42,875 [COUGH] 316 00:18:42,875 --> 00:18:44,268 The analytical engine. 317 00:18:44,268 --> 00:18:49,423 This is what Ada described. 318 00:18:49,423 --> 00:18:54,275 This is plan 28, 1840, which is more or less the state of the engine 319 00:18:54,275 --> 00:18:58,047 at the time Ada entered the scene in a very intensive way. 320 00:18:58,047 --> 00:19:00,687 When she started studying mathematics again, 321 00:19:00,687 --> 00:19:04,982 returning to mathematics having got married and having had three children. 322 00:19:04,982 --> 00:19:09,719 And this would be roughly the state of the engine which that Ada had in her mind 323 00:19:09,719 --> 00:19:13,585 when she was describing the machine and writing her notes. 324 00:19:13,585 --> 00:19:16,882 And we'll just briefly look at some of the features of it. 325 00:19:16,882 --> 00:19:19,953 It is the best known of the drawings because Babbage actually there are very 326 00:19:19,953 --> 00:19:22,258 few drawings that get an overview of the entire system. 327 00:19:22,258 --> 00:19:24,375 So, we just looked at some of it's features. 328 00:19:24,375 --> 00:19:27,982 This huge central area is the mole, which we now call a central processor. 329 00:19:27,982 --> 00:19:32,658 The linear area on the right is called the store, which we would call memory now. 330 00:19:32,658 --> 00:19:36,151 The physical scale of this is absolutely astronomical, well, 331 00:19:36,151 --> 00:19:38,034 not literally but figuratively. 332 00:19:38,034 --> 00:19:39,858 This is about six foot across in diameter. 333 00:19:39,858 --> 00:19:41,782 The mole, it's about 15 foot high. 334 00:19:41,782 --> 00:19:42,807 There were 17. 335 00:19:42,807 --> 00:19:44,974 The store here, if we look at each of these, so this is the plan, 336 00:19:44,974 --> 00:19:46,189 it's looking down on the machine. 337 00:19:46,189 --> 00:19:49,101 So each of these circles is a column of figure wheels. 338 00:19:49,101 --> 00:19:51,701 So v1, v2, these are called variables, 339 00:19:51,701 --> 00:19:55,159 are columns of figure wheels in the store, in the memory. 340 00:19:55,159 --> 00:19:57,254 So each of these things is a column, and we need to know that. 341 00:19:57,254 --> 00:20:01,035 And I'm gonna ask you just to remember this brief configuration here of 342 00:20:01,035 --> 00:20:04,824 the memory because we're gonna map this onto Ada's program. 343 00:20:04,824 --> 00:20:08,604 And so, there's the mole which is the central process, 344 00:20:08,604 --> 00:20:12,620 the separation of the mole and the store which is a feature for 345 00:20:12,620 --> 00:20:17,666 normal architecture described in 1945 and which is dominated complete 346 00:20:17,666 --> 00:20:22,358 design to the present day that is present and inherent in this design. 347 00:20:22,358 --> 00:20:25,292 And the machine had enormous capability. 348 00:20:25,292 --> 00:20:27,185 It had an internal repertoire of automatic instructions. 349 00:20:27,185 --> 00:20:29,995 So it could do automatically division, multiplication, subtraction, 350 00:20:29,995 --> 00:20:30,668 automatically. 351 00:20:30,668 --> 00:20:41,837 You give it a macro instruction, it did it through internal manipulation. 352 00:20:41,837 --> 00:20:47,448 The store is truncated here for reasons of drafting convenience. 353 00:20:47,448 --> 00:20:51,008 There are 17 registers, v things shown here, a bunch up top and 354 00:20:51,008 --> 00:20:53,484 a bunch on the bottom, but it's truncated. 355 00:20:53,484 --> 00:20:57,495 The machine with 17 variables would be 18 foot long. 356 00:20:57,495 --> 00:21:00,910 Babbage spoke of an entry level machine with 100 variables, 357 00:21:00,910 --> 00:21:02,565 which would be 45 foot long. 358 00:21:02,565 --> 00:21:05,094 And he spoke of machines with 1,000 variables. 359 00:21:05,094 --> 00:21:09,237 You're talking about something extending roughly the width of this theater. 360 00:21:09,237 --> 00:21:13,368 And so, when we talk about a quantum leap in logical conception, and 361 00:21:13,368 --> 00:21:23,263 physical scale, we mean this absolutely literally. 362 00:21:23,263 --> 00:21:27,636 The machine, one of it's revolutionary features was that it could be 363 00:21:27,636 --> 00:21:29,648 programmed using punch cards. 364 00:21:29,648 --> 00:21:31,323 And here's an example of punch cards. 365 00:21:31,323 --> 00:21:38,432 Those cards solve first order simultaneous equations. 366 00:21:38,432 --> 00:21:41,212 The cards on the right are operation cards, 367 00:21:41,212 --> 00:21:44,755 they tell you what arithmetical operation to perform. 368 00:21:44,755 --> 00:21:47,230 The cards on the left are variable cards, 369 00:21:47,230 --> 00:21:50,565 which tell you where in the memory to find the upper end. 370 00:21:50,565 --> 00:21:52,615 Where is what you need operate on to be found and 371 00:21:52,615 --> 00:21:54,148 where should you put the results. 372 00:21:54,148 --> 00:21:57,311 There are other kinds of cards, but those are the main kinds of cards. 373 00:21:57,311 --> 00:22:01,774 And this is one of baggages' card readers, You can see here it's, draped over prism. 374 00:22:01,774 --> 00:22:05,556 They are fan-folded, stitched together with ribbon base board cards, 375 00:22:05,556 --> 00:22:06,959 the pool of cards is there. 376 00:22:06,959 --> 00:22:10,961 And as this prism approaches these levers. 377 00:22:10,961 --> 00:22:13,181 If there is a hole the lever goes through and takes no action. 378 00:22:13,181 --> 00:22:16,339 If there is no hole, the lever is activated. 379 00:22:16,339 --> 00:22:20,095 And so, that is how the communication between punch cards and the machine works 380 00:22:20,095 --> 00:22:23,527 by interrogating whether there is or is not a hole in the series of cards. 381 00:22:23,527 --> 00:22:28,730 And there's many, many of these card readers distributed 382 00:22:28,730 --> 00:22:33,527 around the machine to read the various piece of cards. 383 00:22:33,527 --> 00:22:37,587 And I'm hoping that Sidney Padua in tomorrow's session will show us 384 00:22:37,587 --> 00:22:41,857 some renderings of the complete engine, how it looks like in 3D using, 385 00:22:41,857 --> 00:22:46,527 of which some of these machines are present. 386 00:22:46,527 --> 00:22:49,338 So, we know from Babbage that the notion of punch cards came 387 00:22:49,338 --> 00:22:50,527 from the Jacquard loom. 388 00:22:50,527 --> 00:22:54,410 The Jacquard loom is a way of producing complex fabrics where the pattern of 389 00:22:54,410 --> 00:22:58,111 the fabric is contained in the card. 390 00:22:58,111 --> 00:23:02,491 Now, Lovelace writes, and this is a well known quote of hers, 391 00:23:02,491 --> 00:23:05,291 we may say most aptly that the analytical engine 392 00:23:05,291 --> 00:23:09,831 weaves algebraic patterns just as the Jacquard loom weaves flowers and leaves. 393 00:23:09,831 --> 00:23:12,821 Now, this is usually taken as some poetical flourish. 394 00:23:12,821 --> 00:23:16,831 But there's an absolutely fundamental idea which is not usually associated with 395 00:23:16,831 --> 00:23:21,171 the Jacquard loom that I believe Lovelace, as you shall see later, absolutely grasps. 396 00:23:21,171 --> 00:23:23,736 There's the notion of universality and 397 00:23:23,736 --> 00:23:27,831 of specificity of function, even if I can pronounce that correctly. 398 00:23:27,831 --> 00:23:31,819 The idea is, the machine, the loom can make any pattern. 399 00:23:31,819 --> 00:23:36,121 What specific pattern it produces is in the software, is in the cards. 400 00:23:36,121 --> 00:23:40,133 And loveless understands that the notion of a universal machine, and 401 00:23:40,133 --> 00:23:44,681 specificity of function which is contained in software in programs. 402 00:23:44,681 --> 00:23:49,144 See how that unrolls and unravels and is folded into the concept of. 403 00:23:49,144 --> 00:23:53,271 And so, when she says the analytical engine weaves algebraic patterns 404 00:23:53,271 --> 00:23:57,961 she's talking about a generalized algebra machine that can do 405 00:23:57,961 --> 00:24:02,401 any form of mathematics provided the machine can be programmed to do so. 406 00:24:02,401 --> 00:24:03,971 A poetic flourish it is. 407 00:24:03,971 --> 00:24:09,601 But I believe it actually embodies quite a substantially more profound idea. 408 00:24:09,601 --> 00:24:14,641 The machine can do automatic micro-programming. 409 00:24:14,641 --> 00:24:16,431 This is one of the barrels. 410 00:24:16,431 --> 00:24:17,321 I wont go into that. 411 00:24:17,321 --> 00:24:21,162 But basically, the machine is a fetch-execute-cycle. 412 00:24:21,162 --> 00:24:24,261 And if you say print this, fetch that, do that what ever it does. 413 00:24:24,261 --> 00:24:25,181 It does it automatically. 414 00:24:25,181 --> 00:24:28,421 And it does it using barrels which are, if you like, internal words, 415 00:24:28,421 --> 00:24:29,611 which are these things. 416 00:24:29,611 --> 00:24:32,651 They can be fifty to 100 of these verticals. 417 00:24:32,651 --> 00:24:34,691 There are studs in these verticals. 418 00:24:34,691 --> 00:24:37,911 And as this barrel moves forward it either activates or 419 00:24:37,911 --> 00:24:41,941 does not activate these levers depending or not whether the stud is present. 420 00:24:41,941 --> 00:24:45,511 Now, for instance, whether this stud is present will produce a conditional branch. 421 00:24:45,511 --> 00:24:48,971 If the stud is present when that barrel advances, it will not activate lever C. 422 00:24:48,971 --> 00:24:52,348 If the stud is present, because that lever's flopped into place, 423 00:24:52,348 --> 00:24:53,981 then it will activate that. 424 00:24:53,981 --> 00:24:57,661 And that is a conditional, that is a condition that has been met. 425 00:24:57,661 --> 00:25:00,001 If a condition is met, insert that slug so 426 00:25:00,001 --> 00:25:03,091 when the barrel advances it activates the lever. 427 00:25:03,091 --> 00:25:08,901 If that slug is not inserted, it takes no action at all. 428 00:25:08,901 --> 00:25:12,431 And because this thing is on a fixed cycle, that condition can occur. 429 00:25:12,431 --> 00:25:15,051 So, it can cater for pre-existing conditionals. 430 00:25:15,051 --> 00:25:16,361 It can do multi-wave branches. 431 00:25:16,361 --> 00:25:20,461 There are other branching mechanisms which are down here in the deducing apparatus. 432 00:25:20,461 --> 00:25:21,901 And each time it goes backwards and 433 00:25:21,901 --> 00:25:24,201 forwards the barrel turn into its next word to execute the next word. 434 00:25:24,201 --> 00:25:27,581 And what that next word is depends on the conditionals and the previous word. 435 00:25:27,581 --> 00:25:28,771 So, you can see it's complex. 436 00:25:28,771 --> 00:25:29,521 It's inherent. 437 00:25:29,521 --> 00:25:35,731 That is how it performs its internal, automatic operations. 438 00:25:35,731 --> 00:25:41,611 Now, Babbage was sufficiently advanced in his, 439 00:25:41,611 --> 00:25:45,601 with the design ability to start programming in 1837. 440 00:25:45,601 --> 00:25:47,881 And between 1837 and 441 00:25:47,881 --> 00:25:52,141 1840 he wrote twenty-four programs, which include various examples of which 442 00:25:52,141 --> 00:25:56,181 are the solution of multiple simultaneous equations of preferred order. 443 00:25:56,181 --> 00:26:00,021 He also has recursion, or what he calls recurrence relationships, which require 444 00:26:00,021 --> 00:26:03,441 repeated sequence of operations, cause the machine can actually iterate. 445 00:26:03,441 --> 00:26:08,441 It can back off a sequence of operation cards and back them forward again. 446 00:26:08,441 --> 00:26:11,571 So it can repeat the same sequence of operations multiple times. 447 00:26:11,571 --> 00:26:14,031 It's iteration. 448 00:26:14,031 --> 00:26:16,071 And so, he has recursion. 449 00:26:16,071 --> 00:26:20,803 Three recursion examples in which each next result requires the previous 450 00:26:20,803 --> 00:26:23,761 result and repetition of the same set of calculations. 451 00:26:23,761 --> 00:26:24,331 So, this is 1837. 452 00:26:24,331 --> 00:26:28,061 And we're going to look at some of these programs now. 453 00:26:28,061 --> 00:26:28,871 That's all he ever built. 454 00:26:28,871 --> 00:26:31,781 It's an experimental model under construction at the time 455 00:26:31,781 --> 00:26:33,051 of his death in 1871. 456 00:26:33,051 --> 00:26:35,181 This is one of Babbage's earliest programs. 457 00:26:35,181 --> 00:26:38,526 August 5, August 1837, we're talking about, yeah? 458 00:26:38,526 --> 00:26:40,214 And it's to solve two simultaneous equations, 459 00:26:40,214 --> 00:26:41,581 first order simultaneous equations. 460 00:26:41,581 --> 00:26:44,851 So you would need to solve for x, solve for y, and 461 00:26:44,851 --> 00:26:48,701 eliminate your two variables by substitution, and so on. 462 00:26:48,701 --> 00:26:51,001 So his first program looks like that. 463 00:26:51,001 --> 00:26:51,841 This is his program. 464 00:26:51,841 --> 00:26:53,731 And we're gonna look at, briefly, at the formats. 465 00:26:53,731 --> 00:26:56,331 So, we'll just expand that ringed area which is that. 466 00:26:56,331 --> 00:26:57,571 So, let's look at some of these features. 467 00:26:57,571 --> 00:27:01,527 And this will help us when we get to Ada Lovelace's famous Bernoulli example. 468 00:27:01,527 --> 00:27:03,527 So, and firstly we have line numbers. 469 00:27:03,527 --> 00:27:07,431 Anyone who used a line editor in the old days will recognize that. 470 00:27:07,431 --> 00:27:10,969 You then have what operation is [LAUGH] yes, 471 00:27:10,969 --> 00:27:14,991 there are people who know line editors. 472 00:27:14,991 --> 00:27:17,851 Then there's what next operation is performed. 473 00:27:17,851 --> 00:27:21,061 So, there are four multiplications performed in order, 474 00:27:21,061 --> 00:27:22,926 followed by subtraction or division. 475 00:27:22,926 --> 00:27:23,891 Right. 476 00:27:23,891 --> 00:27:28,139 The next column tells you what variables, what is being acted on. 477 00:27:28,139 --> 00:27:31,951 And there's our reminders up here. 478 00:27:31,951 --> 00:27:33,201 And there we can see V1, V2, V3. 479 00:27:33,201 --> 00:27:37,431 I'll ask you to remember the format of that memory with it's Vs, 480 00:27:37,431 --> 00:27:38,951 with it's vertical content figures. 481 00:27:38,951 --> 00:27:41,271 These are the contents of the various variables. 482 00:27:41,271 --> 00:27:43,431 And the table here tells you what's being operated and 483 00:27:43,431 --> 00:27:45,171 where it's being placed in store. 484 00:27:45,171 --> 00:27:47,941 And just to show you how that maps on to the I thing. 485 00:27:47,941 --> 00:27:50,601 That was the original diagram. 486 00:27:50,601 --> 00:27:53,441 And you can see that V, the variables, that's the stores. 487 00:27:53,441 --> 00:27:55,291 We now call them past registers. 488 00:27:55,291 --> 00:27:58,201 Registers in the store are mapped onto each of these columns which tell you 489 00:27:58,201 --> 00:28:00,341 what is the contents of each at any stage. 490 00:28:00,341 --> 00:28:03,321 So, we have essential features of a program here, 491 00:28:03,321 --> 00:28:06,021 which are it specifies each step of the operation. 492 00:28:06,021 --> 00:28:09,321 It tells you which operation is performed, on what is it performed, and 493 00:28:09,321 --> 00:28:10,991 where the results are placed. 494 00:28:10,991 --> 00:28:13,681 And that is what this diagram does. 495 00:28:13,681 --> 00:28:16,011 Now, in what sense is this a program? 496 00:28:16,011 --> 00:28:18,081 Now, neither Babbage nor Lovelace used that term, nor 497 00:28:18,081 --> 00:28:20,421 do they use words like algorithm. 498 00:28:20,421 --> 00:28:26,131 So, if we look at a very convenient, 499 00:28:26,131 --> 00:28:29,841 a really understandable definition of what a program is is by Tom Hague and 500 00:28:29,841 --> 00:28:33,741 Mark Priestly who said that, program is a single series of instructions that could 501 00:28:33,741 --> 00:28:38,141 be fed into a general purpose computer to automatically control its operation. 502 00:28:38,141 --> 00:28:39,651 Very simple. 503 00:28:39,651 --> 00:28:42,471 This is clearly not a program. 504 00:28:42,471 --> 00:28:45,111 It is a series of arithmetical instructions. 505 00:28:45,111 --> 00:28:46,961 The program is in the cards. 506 00:28:46,961 --> 00:28:49,901 There is no control information in this program. 507 00:28:49,901 --> 00:28:51,841 There's no control information. 508 00:28:51,841 --> 00:28:53,731 It just tells you what the series of instructions are and 509 00:28:53,731 --> 00:28:54,541 it's like a state diagram. 510 00:28:54,541 --> 00:28:56,891 So, it's more accurate to call it perhaps a trace. 511 00:28:56,891 --> 00:28:58,803 And that's a word that Lovelace uses. 512 00:28:58,803 --> 00:29:00,122 Or a simulated trace. 513 00:29:00,122 --> 00:29:01,209 Or a walk through. 514 00:29:01,209 --> 00:29:05,181 Or even a state diagram to tell you what state the machine is in. 515 00:29:05,181 --> 00:29:08,261 But I think there are a number of features that do fit comfortably with the idea 516 00:29:08,261 --> 00:29:09,491 of order programs. 517 00:29:09,491 --> 00:29:13,471 Sequential operation, defined rules and data structure. 518 00:29:13,471 --> 00:29:18,891 And there is, primarily, an algorithmic intention in what this is doing. 519 00:29:18,891 --> 00:29:22,464 So, I don't think we'd be committing a great intellectual crime if we 520 00:29:22,464 --> 00:29:24,963 did continue to refer to this, and Lovelace's, 521 00:29:24,963 --> 00:29:28,058 as a program bearing in mind that our definition of a program is 522 00:29:28,058 --> 00:29:33,527 an anachronistic one based on what we now understand a program to be. 523 00:29:33,527 --> 00:29:40,901 So, finally, we get to Lovelace's sketch, the sketch of the analytical engine. 524 00:29:40,901 --> 00:29:48,301 Firstly, there's one thing we need to do before that. 525 00:29:48,301 --> 00:29:50,901 Babbage disdained to lecture. 526 00:29:50,901 --> 00:29:53,167 He was heckled once when he lectured. 527 00:29:53,167 --> 00:29:56,351 He was, as a young man, he was crippling shy. 528 00:29:56,351 --> 00:29:58,921 And for whatever reason he never lectured in England. 529 00:29:58,921 --> 00:30:03,824 The only time he ever lectured on his analytic engine was in 1840 when he was 530 00:30:03,824 --> 00:30:07,557 invited by Giovanni Plana to attend a convention in Turin. 531 00:30:07,557 --> 00:30:08,932 And there he expounded on his analytical engine. 532 00:30:08,932 --> 00:30:12,786 Present was Luigi Menabrea, an Italian engineer, 533 00:30:12,786 --> 00:30:16,028 subsequently the Prime Minister of Italy, 534 00:30:16,028 --> 00:30:21,819 who then wrote an article in French, published in 1842 of a description. 535 00:30:21,819 --> 00:30:25,147 And included in Menabrea's paper are two programs, and 536 00:30:25,147 --> 00:30:28,621 they're exactly the examples from Babbage's 1832. 537 00:30:28,621 --> 00:30:34,311 That's Menabrea's logical translated new English by Lovelace, 538 00:30:34,311 --> 00:30:35,341 and a tiny alteration. 539 00:30:35,341 --> 00:30:39,287 But that's effectively the format of Menabrea's program. 540 00:30:39,287 --> 00:30:43,354 Which was taken directly, it's the same example of solving two linear simultaneous 541 00:30:43,354 --> 00:30:45,625 equations, from Babbage's 1837 thing. 542 00:30:45,625 --> 00:30:49,575 So Babbage went to Tyrone, explained things, used these as examples, and 543 00:30:49,575 --> 00:30:53,587 this is embodied in the first publication which Lovelace, as you shall see, 544 00:30:53,587 --> 00:30:55,087 subsequently translated. 545 00:30:55,087 --> 00:31:01,727 So we come finally to, what did Ada do? 546 00:31:01,727 --> 00:31:07,009 Let's get the time frame straight. 547 00:31:07,009 --> 00:31:10,931 So, Lovelace is born 1815. 548 00:31:10,931 --> 00:31:13,171 She married William King, 1835. 549 00:31:13,171 --> 00:31:17,851 She was then Ada Byron and then she became Ada Augusta King. 550 00:31:17,851 --> 00:31:21,734 And in 1838, William King was elevated to an earldom. 551 00:31:21,734 --> 00:31:26,511 and so Ada Byron, Ada King, became Ada, Countess of Lovelace. 552 00:31:26,511 --> 00:31:31,121 That is the account for the multiple names by which she's known by. 553 00:31:31,121 --> 00:31:34,949 And the period we're talking about is the period in which she wrote the notes, 554 00:31:34,949 --> 00:31:37,501 which is 1843, six months between February and 555 00:31:37,501 --> 00:31:39,769 August there was this starburst of activity. 556 00:31:39,769 --> 00:31:42,185 Where Ada and Babbage, where Lovelace and 557 00:31:42,185 --> 00:31:46,749 Babbage were involved in a frenetic collaboration involving sometimes three or 558 00:31:46,749 --> 00:31:51,331 four exchanges per day in addition to visits, during which Ada wrote the notes. 559 00:31:51,331 --> 00:31:55,762 So Ada translated Menebrea's article, possibly on the suggestion of Wheatstone, 560 00:31:55,762 --> 00:31:57,991 without Babbage's knowledge. 561 00:31:57,991 --> 00:32:00,244 Babbage is presented with his fait accompli and 562 00:32:00,244 --> 00:32:02,731 he says why didn't you write an article of your own? 563 00:32:02,731 --> 00:32:05,231 And she said it never occurred to her, and he said add the notes and 564 00:32:05,231 --> 00:32:09,991 that is how Peter's famous sketch came to be. 565 00:32:09,991 --> 00:32:19,021 So we're talking about that six month period of extraordinary collaboration. 566 00:32:19,021 --> 00:32:23,355 During that period, their relationship is very interesting, she becomes bossy, 567 00:32:23,355 --> 00:32:27,851 coquettish, she's self exalting about the excellence of her own work. 568 00:32:27,851 --> 00:32:31,555 She gives him stern instructions, she badgers him for explanations, and 569 00:32:31,555 --> 00:32:34,513 she threatens him with her annoyance if he does not comply. 570 00:32:34,513 --> 00:32:37,911 And if he mixes up her draft and makes gratuitous alterations. 571 00:32:37,911 --> 00:32:40,216 It was a very friendly, productive collaboration. 572 00:32:40,216 --> 00:32:42,551 >> [LAUGH] >> And 573 00:32:42,551 --> 00:32:44,751 there was no ill intent in it at all, except for 574 00:32:44,751 --> 00:32:48,391 one spat which had nothing to do actually with the content of the material. 575 00:32:48,391 --> 00:32:52,161 So Sketch was published in August 1843 in Taylors Scientific Memoirs and 576 00:32:52,161 --> 00:32:55,311 Lovelace was 26 years old at the time. 577 00:32:55,311 --> 00:32:57,941 Babbage, as we said, was 42 when Lovelace was 17. 578 00:32:57,941 --> 00:33:02,341 Babbage was one year older than Ada's mother. 579 00:33:02,341 --> 00:33:05,473 And finally the famous paper, Scientific Memoirs, 580 00:33:05,473 --> 00:33:10,021 it was a journal which specialized in bringing to English speaking readers 581 00:33:10,021 --> 00:33:14,261 foreign scientific papers and Wheatstone actually sat on the committee that was 582 00:33:14,261 --> 00:33:16,321 responsible, if you like for lobbying for 583 00:33:16,321 --> 00:33:20,431 material, which is possibly the roots of his suggestion that Ada should do this. 584 00:33:20,431 --> 00:33:22,861 The title bears Menabrea's name. 585 00:33:22,861 --> 00:33:25,041 It does not include Lovelace's name. 586 00:33:25,041 --> 00:33:30,501 But, each of the seven notes, notes A to G, that Lovelace included are signed with 587 00:33:30,501 --> 00:33:35,883 her initials, AAL, except for the last one which is signed ALL, which is a typo. 588 00:33:35,883 --> 00:33:39,651 >> [LAUGH] >> So 589 00:33:39,651 --> 00:33:42,289 we can see that, from the page numbering, 590 00:33:42,289 --> 00:33:47,641 that the length of Ada's notes is twice the length of Menabrea's original paper. 591 00:33:47,641 --> 00:33:51,124 Babbage says it's three times, but I counted them, not the words, but 592 00:33:51,124 --> 00:33:54,688 the pages. 593 00:33:54,688 --> 00:34:01,271 The note's essentially expansions and elaborations of Menabrea's article. 594 00:34:01,271 --> 00:34:03,701 With two exceptions, mostly note A and note G. 595 00:34:03,701 --> 00:34:06,141 Note A is philosophical, which is of interest to us, and 596 00:34:06,141 --> 00:34:08,556 note G is the Bernoulli example, which we're now gonna look at them. 597 00:34:08,556 --> 00:34:13,721 Then we're going to return to note A, which is the philosophical side. 598 00:34:13,721 --> 00:34:14,711 This is the Bernoulli formula. 599 00:34:14,711 --> 00:34:18,261 It doesn't matter if that means nothing to you, and right now 600 00:34:18,261 --> 00:34:21,811 sitting there is responsible for that nice form of that particular equation, 601 00:34:21,811 --> 00:34:22,681 because Lovelace does not include it. 602 00:34:22,681 --> 00:34:26,071 This is the formula that Lovelace derives, doesn't matter how. 603 00:34:26,071 --> 00:34:27,281 This is the Bernoulli expression. 604 00:34:27,281 --> 00:34:29,421 What she's calculating is B. 605 00:34:29,421 --> 00:34:33,851 Each next B in the series defined by that, for which you need all prior Bs and 606 00:34:33,851 --> 00:34:38,971 have to recalc all the prior known, already calculated Bernoulli numbers, 607 00:34:38,971 --> 00:34:43,651 which you then produce a weighted sum by these As, 608 00:34:43,651 --> 00:34:47,871 which are the coefficients, which have to be recalculated for each Bernoulli number. 609 00:34:47,871 --> 00:34:48,951 So that's actually, 610 00:34:48,951 --> 00:34:54,351 it's an ambitious calculation to do, computationally and manually. 611 00:34:54,351 --> 00:34:58,923 Bernoulli numbers were known from the 18th century, five minutes, I'm in trouble. 612 00:34:58,923 --> 00:35:02,557 >> [LAUGH] >> Thank you. 613 00:35:02,557 --> 00:35:03,939 Bernoulli numbers were known quite well. 614 00:35:03,939 --> 00:35:04,937 They were calculated by hand. 615 00:35:04,937 --> 00:35:08,420 They were published first in 1713. 616 00:35:08,420 --> 00:35:16,350 So, we'll now look at the choice of the Bernoulli example was Lovelace's, 617 00:35:16,350 --> 00:35:22,572 even though Babbage had written to Humboldt earlier on about 618 00:35:22,572 --> 00:35:27,575 using the engine to count out the newly numbers. 619 00:35:27,575 --> 00:35:32,505 So, Lovelace writes to Babbage and said, I have it in mind to include a Bernoulli 620 00:35:32,505 --> 00:35:36,942 number in one of my notes, send me, she says, the data and the formula. 621 00:35:36,942 --> 00:35:40,341 Sounds like an imperious thing, but it is actually a friendly request. 622 00:35:40,341 --> 00:35:42,901 And the date of that is slightly uncertain, but 623 00:35:42,901 --> 00:35:46,371 it's thought to be around May, and if you go back to Babbage's scribbling books, 624 00:35:46,371 --> 00:35:50,701 on the seventh of May, we see his thoughts lingering with Bernoulli's numbers. 625 00:35:50,701 --> 00:35:54,881 And Babbage records that he sent this to Ada, and 626 00:35:54,881 --> 00:35:59,091 Ada sent them back to him, because they found a grave mistake. 627 00:35:59,091 --> 00:36:00,891 And if we look at the thing there are two mistakes. 628 00:36:00,891 --> 00:36:04,631 One is the relationship of that term is ambiguous. 629 00:36:04,631 --> 00:36:06,671 It should be present, but it's crossed out. 630 00:36:06,671 --> 00:36:10,841 And if we go to the next slide, that coefficient is wrong. 631 00:36:10,841 --> 00:36:15,651 So just the people were puzzling what the reference to the error was, was, 632 00:36:15,651 --> 00:36:17,661 I believe that is the error. 633 00:36:17,661 --> 00:36:21,471 So, let's get on with the thing, the actual program. 634 00:36:21,471 --> 00:36:23,786 This is what the fuss is all about. 635 00:36:23,786 --> 00:36:27,862 >> [LAUGH] >> This is Ada's program. 636 00:36:27,862 --> 00:36:32,171 [INAUDIBLE] of the Bernoulli's number solution, 637 00:36:32,171 --> 00:36:37,591 calculating that equation and we can see it has all 638 00:36:37,591 --> 00:36:42,001 the essential features of the Menabrea, which is derived Menabrea example, 639 00:36:42,001 --> 00:36:47,971 which are derived from Babbage's programs from six, seven years earlier. 640 00:36:47,971 --> 00:36:50,411 So let's just look more closely at that. 641 00:36:50,411 --> 00:36:52,211 We can see the same structure. 642 00:36:52,211 --> 00:36:56,801 The linear where the variables are, or how they're arranged in the store. 643 00:36:56,801 --> 00:36:59,211 And we can map that exactly as we mapped the other one. 644 00:36:59,211 --> 00:37:00,461 That's mapped in to it, and so on. 645 00:37:00,461 --> 00:37:08,191 The essential information is all there. 646 00:37:08,191 --> 00:37:13,741 There's an index, a double index which is in line two. 647 00:37:13,741 --> 00:37:17,941 If we just look at line two very briefly. 648 00:37:17,941 --> 00:37:23,471 This says, the contents of in register four subtract the contents, 649 00:37:23,471 --> 00:37:27,801 subtract the contents of register one, variable one from the contents of 650 00:37:27,801 --> 00:37:29,961 variable in register four and put it in variable four. 651 00:37:29,961 --> 00:37:33,731 So your overwriting one of the upper rands with the result. 652 00:37:33,731 --> 00:37:35,941 They have no notation to do this. 653 00:37:35,941 --> 00:37:39,171 And there's the double notation, the leading and 654 00:37:39,171 --> 00:37:43,811 trailing index is a way of following what Lovelace calls 655 00:37:43,811 --> 00:37:47,421 an index of location which is where it is, which is the bottom index. 656 00:37:47,421 --> 00:37:50,681 And an index of alteration which is the upper index. 657 00:37:50,681 --> 00:37:54,011 And if we look at that, this is what they were trying to avoid. 658 00:37:54,011 --> 00:37:55,931 Mathematicians hated statements of that kind. 659 00:37:55,931 --> 00:37:59,134 It was an offense against mathematical identity. 660 00:37:59,134 --> 00:38:03,534 So we have a flag here, that in order to code computers you needed a new notation. 661 00:38:03,534 --> 00:38:05,693 There are other ways of doing it, could be an assignment arrow. 662 00:38:05,693 --> 00:38:10,022 And they were so concerned about this that Victorians actually invented emoticons to 663 00:38:10,022 --> 00:38:10,814 express this. 664 00:38:10,814 --> 00:38:13,588 >> [LAUGH]. 665 00:38:13,588 --> 00:38:17,590 >> And that is the form that Ada uses, which is leading and 666 00:38:17,590 --> 00:38:22,027 trailing index To show the index of location, where it is and 667 00:38:22,027 --> 00:38:26,986 index of alterations so that V4, the contents of variable four has 668 00:38:26,986 --> 00:38:31,421 been changed in the process of that calculation. 669 00:38:31,421 --> 00:38:37,391 And Bernard, who follows this session if I ever finish immediately will 670 00:38:37,391 --> 00:38:44,151 be elaborating on aspects of the iteration, so let me wind up now. 671 00:38:44,151 --> 00:38:47,691 Okay, where does that magnificent notation come from? 672 00:38:47,691 --> 00:38:50,921 All right, we go back to Babbage's thing and we look in this little table and 673 00:38:50,921 --> 00:38:53,841 there is the double index. 674 00:38:53,841 --> 00:38:57,901 And he used Roman numerals and not, later he changed them to new. 675 00:38:57,901 --> 00:39:01,411 But the point is in his earliest programs he already saw the need for a notation, 676 00:39:01,411 --> 00:39:05,091 or the notational need for showing index of alteration. 677 00:39:05,091 --> 00:39:08,051 Say how do you express the fact that something had changed, 678 00:39:08,051 --> 00:39:12,151 how can you track back, how through all, what the contents of that register 679 00:39:12,151 --> 00:39:16,391 had been through the history, through the trajectory of the calculation. 680 00:39:16,391 --> 00:39:22,031 So let me get to what I'm getting at here. 681 00:39:22,031 --> 00:39:27,407 The seemingly dismal conclusion is that it is very difficult to identify features, 682 00:39:27,407 --> 00:39:31,871 Lovelace's Bernoulli example that do not have precedence in 683 00:39:31,871 --> 00:39:36,441 Babbage's earliest programming examples, or the derivative example to Menabrea. 684 00:39:36,441 --> 00:39:39,561 It is very difficult to find any feature of this that is not been. 685 00:39:39,561 --> 00:39:41,051 Now I'd like to emphasize, 686 00:39:41,051 --> 00:39:46,558 that the purpose of doing this is not to discredit Ada [LAUGH] Lovelace. 687 00:39:46,558 --> 00:39:51,401 [COUGH] Ada Lovelace, never made any claim to be the first programmer. 688 00:39:51,401 --> 00:39:55,251 She makes no claim for having any precedence for being responsible for 689 00:39:55,251 --> 00:39:57,471 any precedence any creation of programs. 690 00:39:57,471 --> 00:40:01,731 This is a construction, it's a confection, of our modern age. 691 00:40:01,731 --> 00:40:06,431 And I say this is not directed at Lovelace, who is blameless in this. 692 00:40:06,431 --> 00:40:08,291 It is directed at people who have followed and 693 00:40:08,291 --> 00:40:11,011 perpetuated this particular perception. 694 00:40:11,011 --> 00:40:13,131 As an historian, I can be offended but 695 00:40:13,131 --> 00:40:16,521 I can be offended in the privacy of my own attic. 696 00:40:16,521 --> 00:40:20,981 There is something more important to be offended about here, that to focus and 697 00:40:20,981 --> 00:40:25,791 to concentrate on Lovelace as the first programmer, masks actually what her real 698 00:40:25,791 --> 00:40:29,401 contribution was which I would argue is vastly more important than adding yet 699 00:40:29,401 --> 00:40:33,831 another example to Babbage's pre-existing set of programs. 700 00:40:33,831 --> 00:40:42,691 And I will conclude by saying what it is I think Lovelace's three contributions are. 701 00:40:42,691 --> 00:40:46,971 Apart from the fact it's contradicted by history, the first program thing, 702 00:40:46,971 --> 00:40:48,071 this is what I believe Lovelace, 703 00:40:48,071 --> 00:40:52,301 which is masked by this obsession with this Bernoulli program. 704 00:40:52,301 --> 00:40:54,581 First, the leap from calculation to computing, 705 00:40:54,581 --> 00:40:56,751 which is a leap that Lovelace did and nobody else did. 706 00:40:56,751 --> 00:41:00,361 Secondly, the recognition that computers are difference in kind 707 00:41:00,361 --> 00:41:02,321 from anything that had gone before. 708 00:41:02,321 --> 00:41:07,511 Finally, the kind of discourse that sketch represents. 709 00:41:07,511 --> 00:41:13,201 So firstly, the transition, [COUGH] excuse me, from calculation to computing. 710 00:41:13,201 --> 00:41:14,931 It was Lovelace who articulated for 711 00:41:14,931 --> 00:41:20,361 the first time that number could represent entity other than quantity. 712 00:41:20,361 --> 00:41:24,741 She speaks that number could represent letter of the alphabet, note of music. 713 00:41:24,741 --> 00:41:26,829 It was she who saw that the power and 714 00:41:26,829 --> 00:41:31,077 potential of computers lay in the ability of the machine to manipulate 715 00:41:31,077 --> 00:41:34,536 the representations of the world contained in symbols. 716 00:41:34,536 --> 00:41:38,773 She made the connection between the machine and the world. 717 00:41:38,773 --> 00:41:43,981 [COUGH] Machines can only operate on numbers. 718 00:41:43,981 --> 00:41:46,761 If we assign meaning to those numbers the machine operates on the numbers. 719 00:41:46,761 --> 00:41:50,521 We map those meanings back and the machine is saying something about the world. 720 00:41:50,521 --> 00:41:53,101 So those simple ideas it's very difficult to put yourself in a position to the point 721 00:41:53,101 --> 00:41:56,901 which that wasn't true but and then it wasn't and we'll see presently or 722 00:41:56,901 --> 00:41:57,851 very briefly why. 723 00:41:57,851 --> 00:42:02,111 So she wrote, the machine might act on other things besides numbers posing for 724 00:42:02,111 --> 00:42:04,331 instance that the fundamental relations that pitch sounds and 725 00:42:04,331 --> 00:42:05,301 the science of harmony and 726 00:42:05,301 --> 00:42:08,471 music composition were susceptible to such expressions and adaptations. 727 00:42:08,471 --> 00:42:11,011 The engine might compose elaborate scientific piece of music and 728 00:42:11,011 --> 00:42:16,181 any degree of place in extent, so that's a well known quote of hers. 729 00:42:16,181 --> 00:42:18,691 Now, what's the choice of notes traditions 730 00:42:18,691 --> 00:42:20,741 because there's a quantitive relation between frequency and 731 00:42:20,741 --> 00:42:25,931 pitch, is there a trick here, that this is not a generalized thing? 732 00:42:25,931 --> 00:42:29,375 This is not generalized thing, there is enough in there to 733 00:42:29,375 --> 00:42:34,368 show on very close reading that if central idea of symbolic representation of things 734 00:42:34,368 --> 00:42:37,342 other than number is present and can be defended. 735 00:42:37,342 --> 00:42:41,671 Secondly, that is historically known on different kind [COUGH] she wrote that 736 00:42:41,671 --> 00:42:45,135 the analytical engine does not occupy common ground with mere 737 00:42:45,135 --> 00:42:48,543 calculating machines, it holds a position wholly its own. 738 00:42:48,543 --> 00:42:51,996 And if we jump to Minsky, 1967, Minsky's saying of computer and 739 00:42:51,996 --> 00:42:55,041 computer like machines, neither history nor philosophy nor 740 00:42:55,041 --> 00:42:58,084 common sense will tell us how these machines will effect us for 741 00:42:58,084 --> 00:43:02,469 they do not work as did the machines of the Industrial Revolution. 742 00:43:02,469 --> 00:43:07,139 This is LoveLace, seeing the difference between the two specific function and 743 00:43:07,139 --> 00:43:11,809 universality of the touring condor most that she saw embodied in the jack-eyed 744 00:43:11,809 --> 00:43:15,989 loom which is why that poetic flourished about how the break patterns, 745 00:43:15,989 --> 00:43:17,121 I'm nearly done. 746 00:43:17,121 --> 00:43:21,522 [COUGH] Finally, what kind of discourse this is, the moment we start reading 747 00:43:21,522 --> 00:43:26,129 the notes, we all lifted our job the technocentric writing of Babbage about his 748 00:43:26,129 --> 00:43:30,696 engines into a different conceptual discourse, we are talking about ideas. 749 00:43:30,696 --> 00:43:34,259 Lovelace is asking, what does this machine signify? 750 00:43:34,259 --> 00:43:35,491 What does it mean? 751 00:43:35,491 --> 00:43:38,591 And to what extent is what it signifies important? 752 00:43:38,591 --> 00:43:40,761 No where in his published writing or 753 00:43:40,761 --> 00:43:44,501 any of the manuscripts that I've looked at does Babbage right in this way. 754 00:43:44,501 --> 00:43:48,512 Nowhere does he talk about the engine outside mathematics, 755 00:43:48,512 --> 00:43:50,091 being bound by number. 756 00:43:50,091 --> 00:43:55,651 [COUGH] Extraordinary in the scope and scale of his work. 757 00:43:55,651 --> 00:43:59,162 There is that dimension which is not there. 758 00:43:59,162 --> 00:44:01,229 How was Babbage influenced by Lovelace? 759 00:44:01,229 --> 00:44:03,601 This is the very last little bit. 760 00:44:03,601 --> 00:44:06,981 Babbage was very much taken with her ideas and to the extent that actually, 761 00:44:06,981 --> 00:44:08,461 about note A and note G specifically, 762 00:44:08,461 --> 00:44:10,791 and to the extent that he didn't want to actually return her drafts. 763 00:44:10,791 --> 00:44:14,051 He wanted to keep them and he writes to her, 764 00:44:14,051 --> 00:44:16,771 said I'm loathe to send these back to you. 765 00:44:16,771 --> 00:44:19,321 And he wrote, Babbage writes, the more I read your notes, 766 00:44:19,321 --> 00:44:23,681 the more surprised I am at them and regret at not having earlier explored so 767 00:44:23,681 --> 00:44:26,151 rich a vein in the noblest metal. 768 00:44:26,151 --> 00:44:28,871 So he's saying, golly, these are marvelous things. 769 00:44:28,871 --> 00:44:32,241 If he was influenced at all, there is not the slightest evidence for it. 770 00:44:32,241 --> 00:44:38,382 Not at all, because in 1869, two years before his death, he sat down. 771 00:44:38,382 --> 00:44:40,551 Well, I'm assuming he wrote when he was sitting. 772 00:44:40,551 --> 00:44:45,107 And he attempted to describe the general description of the engine and 773 00:44:45,107 --> 00:44:48,016 three times he's tried to, in May and December. 774 00:44:48,016 --> 00:44:52,120 1869, two years before death, he tried to convey to the world what the purpose of 775 00:44:52,120 --> 00:44:57,431 this engine was and each one starts with, we can get there. 776 00:44:57,431 --> 00:45:01,216 The general description of the analytical engine, May, 1869, and 777 00:45:01,216 --> 00:45:02,861 we can blow that up. 778 00:45:02,861 --> 00:45:05,951 And he says, the object of this engine is to execute by machinery, 779 00:45:05,951 --> 00:45:07,121 all the operations of arithmetic, 780 00:45:07,121 --> 00:45:11,291 all the operations analysis and print any or all of the calculated results. 781 00:45:11,291 --> 00:45:14,581 There is nothing, other than mathematics in his conception. 782 00:45:14,581 --> 00:45:21,707 This is after 50 years of mature contemplation. 783 00:45:21,707 --> 00:45:27,391 So, it's Lovelace who made the connection between the world and the machine. 784 00:45:27,391 --> 00:45:30,081 If we return to the forgotten title of this thing which is 785 00:45:30,081 --> 00:45:31,461 Two Visions of Computer. 786 00:45:31,461 --> 00:45:36,061 We have Lovelace's vision, which I've described as the ability of the machine to 787 00:45:36,061 --> 00:45:39,401 manipulate according to rules, reputation of the world containing symbols and 788 00:45:39,401 --> 00:45:45,741 we have Babbage's conception which is boundaried by mathematics. 789 00:45:45,741 --> 00:45:49,345 So we have Lovelace who sees the potential of the machine with an outreach way beyond 790 00:45:49,345 --> 00:45:52,190 the boundaries that Babbage sees, and way beyond mathematics. 791 00:45:52,190 --> 00:45:57,250 And it's for these ideas that Ada Augusta, Countess of Lovelace, 792 00:45:57,250 --> 00:46:00,642 deserves to be celebrated as fully as she is. 793 00:46:00,642 --> 00:46:01,281 Thank you. 794 00:46:01,281 --> 00:46:07,435 >> [APPLAUSE]