Полная расшифровка выпуска Numerics.NET with Jeffrey Sax

at all. 42 00:02:04.719 --> 00:02:08.039 I am. Yeah, especially last 2018 was just dark. 43 00:02:08.419 --> 00:02:09.939 Just depressing. Yeah. 44 00:02:10.259 --> 00:02:12.740 So I will have some bad news too, but for 45 00:02:12.780 --> 00:02:16.710 some good. The world's first malaria vaccine began rolling out 46 00:02:16.750 --> 00:02:17.610 in Africa. 47 00:02:17.710 --> 00:02:18.069 Exciting. 48 00:02:18.169 --> 00:02:22.810 Malawi, Ghana, and Kenya began vaccinating children with RTSS, the 49 00:02:22.870 --> 00:02:25.780 first malaria vaccine used in a large-scale public health program. 50 00:02:26.729 --> 00:02:30.000 Our friend Bill Gates and Melinda Gates were behind that. 51 00:02:30.680 --> 00:02:32.840 I don't know if they're actually our friends, but we've 52 00:02:33.180 --> 00:02:40.210 seen them. Yeah, I met them. About 360,000 children per 53 00:02:40.250 --> 00:02:43.090 year were expected to receive it during the pilot. So cool. 54 00:02:44.090 --> 00:02:49.180 Ethiopia and Eritrea's peace efforts received the Nobel Peace Prize. 55 00:02:50.060 --> 00:02:50.539 Very good. 56 00:02:50.740 --> 00:02:53.599 Those two have been at loggerheads since their formations. 57 00:02:53.759 --> 00:02:54.020 Yeah. 58 00:02:54.319 --> 00:02:58.500 And see, it is possible. Nearly 100 captive whales and 59 00:02:58.659 --> 00:03:02.740 orcas were returned to the wild. Russian authorities gradually released 60 00:03:02.819 --> 00:03:06.699 animals from the notorious whale jail in the country's far east. 61 00:03:07.240 --> 00:03:10.400 By November, the remaining 50 beluga whales had been freed, 62 00:03:10.460 --> 00:03:11.939 completing the operation. 63 00:03:12.139 --> 00:03:12.319 Wow. 64 00:03:12.490 --> 00:03:18.849 Reminds me of Star Trek IV. Algeria and Argentina eliminated malaria. 65 00:03:19.189 --> 00:03:21.889 Eliminated. How cool is that? Well, there's a bunch of 66 00:03:21.909 --> 00:03:23.449 ways to tackle that, right? Like you can do it 67 00:03:23.490 --> 00:03:29.000 by just controlling mosquitoes. Yeah. But also, you know, handing 68 00:03:29.069 --> 00:03:31.300 out nets. Like there's all kinds of tools to try. 69 00:03:31.539 --> 00:03:36.020 And it all works together. Ethiopia launched a massive tree 70 00:03:36.080 --> 00:03:42.110 planting campaign. Millions participated in the country's green legacy reforestation effort. 71 00:03:42.770 --> 00:03:46.909 The Ethiopian government reported that roughly 350 million seedlings were 72 00:03:46.949 --> 00:03:49.469 planted in a single day in July, part of a 73 00:03:49.509 --> 00:03:54.389 campaign aimed at planting billions of trees. The exact single-day 74 00:03:54.509 --> 00:04:01.069 figure wasn't independently verified, but the enormous public participation was real. So, 75 00:04:01.569 --> 00:04:04.669 now let's get to the depressing stuff. Well, maybe not depressing, 76 00:04:04.710 --> 00:04:08.159 but you know. Donald Trump is impeached. For the first time. 77 00:04:08.379 --> 00:04:13.909 Depressing? It's up to you, I think. Hong Kong pro-democracy protests. 78 00:04:14.009 --> 00:04:14.669 Do not go well. 79 00:04:14.729 --> 00:04:16.089 What began as... What's that? 80 00:04:16.189 --> 00:04:17.009 Do not go well. 81 00:04:17.269 --> 00:04:17.470 No. 82 00:04:17.970 --> 00:04:21.149 What began as opposition to an extradition bill grew into 83 00:04:21.209 --> 00:04:26.889 enormous demonstrations demanding democratic reforms and resistance to Beijing's increasing influence. 84 00:04:27.600 --> 00:04:30.899 The protests continued for months and frequently resulted in violent 85 00:04:30.920 --> 00:04:38.139 clashes with the police. Brexit crisis and Boris Johnson's rise. Richard, 86 00:04:38.379 --> 00:04:41.519 do you remember we were sitting in a restaurant somewhere 87 00:04:41.540 --> 00:04:44.660 and you looked over and you said, hey, that's Boris Johnson. 88 00:04:45.199 --> 00:04:46.819 Do you remember that? It was in London. 89 00:04:46.839 --> 00:04:47.240 Yeah. 90 00:04:47.360 --> 00:04:48.480 We were at NDC London. 91 00:04:48.639 --> 00:04:48.800 Yeah. 92 00:04:48.860 --> 00:04:51.139 And you're like, that's Boris Johnson. And I said. 93 00:04:51.220 --> 00:04:51.959 He was in the restaurant. 94 00:04:52.370 --> 00:04:56.310 I said, who? Because I didn't know. 95 00:04:56.470 --> 00:04:58.629 He was the mayor of London one point. And he 96 00:04:58.649 --> 00:05:00.550 was kind of funny when he was the mayor of London. 97 00:05:00.569 --> 00:05:01.589 The quirky guy. 98 00:05:01.949 --> 00:05:05.009 I think this was before his further rise, so I 99 00:05:05.069 --> 00:05:06.069 really didn't know who he was. 100 00:05:06.110 --> 00:05:07.970 Before he was prime minister. Yeah. 101 00:05:08.069 --> 00:05:11.209 But, you know, we did see him. Theresa May repeatedly 102 00:05:11.250 --> 00:05:13.920 failed to get her Brexit agreement through parliament and resigned. 103 00:05:14.420 --> 00:05:17.720 Boris Johnson became prime minister, negotiated a revised deal, and 104 00:05:17.759 --> 00:05:24.779 then won a huge conservative majority in December. Christchurch mosque massacres. 105 00:05:25.100 --> 00:05:29.819 Bad news. This was in New Zealand, your home country. 106 00:05:30.250 --> 00:05:34.509 A white supremacist attacked two mosques in Christchurch on March 15th, 107 00:05:34.550 --> 00:05:38.009 killing 51 people. But the massacre led New Zealand to 108 00:05:38.100 --> 00:05:39.480 rapidly tighten its gun laws. 109 00:05:39.629 --> 00:05:40.319 Yeah, what a concept. 110 00:05:40.740 --> 00:05:44.860 Notre Dame Cathedral set ablaze on April 15th. 111 00:05:44.879 --> 00:05:45.639 It was an accident. 112 00:05:45.740 --> 00:05:46.019 Yeah. 113 00:05:46.579 --> 00:05:50.420 On April 15th, the world watched as the 850-year-old cathedral 114 00:05:50.480 --> 00:05:54.319 in Paris burned. Its famous spire collapsed and much of 115 00:05:54.339 --> 00:05:57.180 the medieval roof was

destroyed, although firefighters managed to save 116 00:05:57.199 --> 00:06:00.990 the main structure. And many important artworks and relics. And 117 00:06:01.410 --> 00:06:03.769 they rebuilt it. It is rebuilt now, yeah. I haven't 118 00:06:03.810 --> 00:06:05.660 seen the new one, but it's on my list. And 119 00:06:05.680 --> 00:06:08.699 you can still see the guy in the tower. 120 00:06:08.480 --> 00:06:09.360 Going, yes, master. 121 00:06:09.379 --> 00:06:19.709 Boeing 737 MAX crashes in worldwide grounding. Was this the 122 00:06:19.750 --> 00:06:21.050 beginning of the end for Boeing? 123 00:06:21.750 --> 00:06:24.110 Oh, no. This was towards the end of the end. 124 00:06:24.129 --> 00:06:25.389 Towards the end of the end. 125 00:06:26.230 --> 00:06:27.670 When you get to the point of actually building an 126 00:06:27.790 --> 00:06:30.509 unsafe aircraft and ignoring the fact that your engineers are 127 00:06:30.529 --> 00:06:32.670 telling you it's unsafe until it starts killing people, you 128 00:06:32.750 --> 00:06:33.649 are very lost. 129 00:06:34.000 --> 00:06:38.420 Yeah. Just a couple more. The U.S.-China trade war escalates. 130 00:06:39.959 --> 00:06:46.420 ISIS leader Abu Bakr al-Baghdadi killed. Mass shootings in El 131 00:06:46.480 --> 00:06:53.100 Paso and Dayton, Ohio. And worldwide protest movements erupt. Beyond 132 00:06:53.139 --> 00:07:02.509 Hong Kong, 2019 saw enormous anti-government demonstrations in Chile, Lebanon, Iraq, Algeria, Sudan, Iran, Bolivia, 133 00:07:02.649 --> 00:07:07.329 and Haiti, among others. So, people not happy. 134 00:07:07.790 --> 00:07:08.730 No. Yeah. 135 00:07:09.069 --> 00:07:11.269 You done? Yeah, I guess I'm done. Let me give 136 00:07:11.290 --> 00:07:12.350 you one more grim one. 137 00:07:12.370 --> 00:07:12.870 Okay. 138 00:07:13.069 --> 00:07:16.139 Right at the end of December 2019, authorities in Wuhan, 139 00:07:16.160 --> 00:07:18.120 China report an unusual pneumonia. 140 00:07:18.670 --> 00:07:19.350 Interesting. 141 00:07:19.379 --> 00:07:19.649 Yeah. 142 00:07:19.790 --> 00:07:21.129 That might have been COVID. 143 00:07:21.350 --> 00:07:21.990 Might have been. Yeah. 144 00:07:22.790 --> 00:07:24.910 Yeah, because that's when. 145 00:07:24.829 --> 00:07:27.389 It really started. All right. You ready for some space stuff? Sure. 146 00:07:27.410 --> 00:07:30.290 Go for it. January, the New Horizons spacecraft, the one 147 00:07:30.310 --> 00:07:34.529 that had gone to Pluto, still going, had its next 148 00:07:34.680 --> 00:07:37.720 close flyby to a Kuiper belt object. Today, we call 149 00:07:37.740 --> 00:07:40.699 that Kuiper belt object Arrokoth, although at the time they 150 00:07:40.720 --> 00:07:44.180 called it Ultima Thule. So that's over a billion kilometers 151 00:07:44.279 --> 00:07:47.579 beyond Pluto. That's how fast that thing was moving. And 152 00:07:47.600 --> 00:07:51.100 was basically a primordial solar system object. It was literally 153 00:07:51.220 --> 00:07:54.339 two blobs of rock and ice stuck together in a 154 00:07:54.399 --> 00:07:58.160 very low gravitational space. But, you know, just an extraordinary 155 00:07:58.240 --> 00:08:01.620 scene back to the early history of the solar system 156 00:08:01.689 --> 00:08:05.329 that way. That's 2019. It's been seven more years. New 157 00:08:05.350 --> 00:08:09.329 Horizons is still whizzing out at very high speed. Also 158 00:08:09.389 --> 00:08:13.209 in January, China's Chang'e 4 lander lands on the far 159 00:08:13.269 --> 00:08:15.930 side of the moon. First time ever in the Von 160 00:08:15.970 --> 00:08:21.810 Karman crater. It has the U-2-2 rover on board. I 161 00:08:21.860 --> 00:08:25.000 think that means little rabbit. It will start its exploration 162 00:08:25.040 --> 00:08:29.000 in the previous year. China had also put up their 163 00:08:29.060 --> 00:08:31.310 relay satellite so they could communicate to the far side 164 00:08:31.350 --> 00:08:34.690 of the moon. In February, back on Mars, the Opportunity 165 00:08:34.750 --> 00:08:38.250 Rover finally ends its mission after 15 years. Designed about 166 00:08:38.269 --> 00:08:40.169 the size of a golf cart, designed for operations for 167 00:08:40.169 --> 00:08:45.460 90 days, ran for 15 years. Now, in 2019, it 168 00:08:45.500 --> 00:08:50.320 was when it declared its mission over. Its last communication 169 00:08:50.340 --> 00:08:54.710 was actually in 2018. There had been a major dust 170 00:08:54.750 --> 00:08:57.889 storm in 2018 on Mars. And that was always the 171 00:08:57.929 --> 00:09:00.590 challenge with these rovers is that there was spirit and opportunities. 172 00:09:00.629 --> 00:09:03.330 They are all solar-based, and so the dust covers up 173 00:09:03.350 --> 00:09:07.389 the solar panels. But the atmosphere of Mars occasionally would 174 00:09:07.450 --> 00:09:11.830 create dust levels that would clean those solar panels off. Classically, 175 00:09:13.549 --> 00:09:16.360 at that time, Opportunity had its own Twitter account, and 176 00:09:16.440 --> 00:09:18.820 so the operators would take the telemetry data and turn 177 00:09:18.840 --> 00:09:22.600 it into text as a tweet from Opportunity. And so 178 00:09:22.620 --> 00:09:26.240 Opportunity's last tweet was, my battery's getting low, and it's 179 00:09:26.279 --> 00:09:28.940 getting dark. Of course, the reality for a device like 180 00:09:28.960 --> 00:09:31.279 that is that if it doesn't have enough power to 181 00:09:31.360 --> 00:09:34.679 keep its electronics warm overnight, those will freeze and it 182 00:09:34.720 --> 00:09:36.960 will not power back up. And that's what happened to Opportunity. Bummer. 183 00:09:37.139 --> 00:09:40.840 In March, the Crew Dragon by SpaceX does its first 184 00:09:41.159 --> 00:09:44.210 flight to the International Space Station. It's completely autonomous. It 185 00:09:44.269 --> 00:09:46.470 actually does its own docking. There's nobody on board. It 186 00:09:46.570

--> 00:09:51.389 works perfectly. It then leaves the station and de-orbits and 187 00:09:51.549 --> 00:09:54.830 lands in the ocean and is recovered successfully. All good news. 188 00:09:55.830 --> 00:09:58.700 Here's the bad news. The following month, that same capsule 189 00:09:58.879 --> 00:10:01.779 is now having an abortion. system test. This was an 190 00:10:01.840 --> 00:10:04.580 unmanned test tethered to the ground firing the Super Dracos 191 00:10:05.100 --> 00:10:08.710 and something goes terribly wrong and the vehicle is destroyed 192 00:10:08.730 --> 00:10:11.870 in the explosion. Bummer. There was a leak in the 193 00:10:11.909 --> 00:10:16.690 helium system for the Super Dracos that created a mass detonation. 194 00:10:17.070 --> 00:10:19.210 NASA actually considered it lucky. It was a huge gift. 195 00:10:19.960 --> 00:10:22.639 You know, you'd hate to have that occur during an 196 00:10:22.759 --> 00:10:27.419 actual flight. It'll delay things for the rest of the year. 197 00:10:27.460 --> 00:10:29.559 They won't flag it until 2020, although that will actually 198 00:10:29.580 --> 00:10:33.470 deliver crew successfully. They'll do a new abort system, use tests, 199 00:10:33.590 --> 00:10:37.769 including an in-flight unmanned abort. Also in April, also on Mars, 200 00:10:37.809 --> 00:10:40.549 the InSight lander will get its first telemetry by measuring 201 00:10:40.590 --> 00:10:43.149 a Mars quake to start mapping the interior of Mars. 202 00:10:43.850 --> 00:10:47.620 So opportunity's done, but the InSight lander's doing its thing. Uh, 203 00:10:47.820 --> 00:10:52.299 also in April, the Israeli nonprofit, uh, company space IL 204 00:10:52.340 --> 00:10:56.279 launched the bear sheet lander, the first commercial privately funded 205 00:10:56.340 --> 00:10:59.440 lunar lander ever flies on a Falcon nine. It originally 206 00:10:59.460 --> 00:11:02.200 been part of the lunar X prize, which started back 207 00:11:02.240 --> 00:11:05.360 in 2017 and 2007 and had ended in 2018. So 208 00:11:05.440 --> 00:11:08.759 it was actually over. It did make it to the moon, 209 00:11:08.820 --> 00:11:12.000 but failed on its landing, which is not that unusual, uh, 210 00:11:12.039 --> 00:11:13.830 because it's really hard to land on the moon. In fact, 211 00:11:14.330 --> 00:11:16.570 Later in the year, in July, India will launch their 212 00:11:16.610 --> 00:11:19.230 Chandran-2 to the moon, and their orbital will work perfectly, 213 00:11:19.250 --> 00:11:22.529 but their Vikram lander will crash on its descent towards 214 00:11:22.570 --> 00:11:28.049 the South Pole. Also in April, the Event Horizon Telescope 215 00:11:28.100 --> 00:11:31.159 publishes the first image of a black hole in the 216 00:11:31.200 --> 00:11:34.960 center of the galaxy, Messier 87. I remember. So this 217 00:11:35.039 --> 00:11:38.500 is using a technology called very long baseline infrometry, where 218 00:11:38.519 --> 00:11:41.879 they actually harness data from a dozen or so different 219 00:11:41.919 --> 00:11:44.750 radio telescopes around the world. to create a sort of 220 00:11:44.909 --> 00:11:48.269 super radio telescope. And then they composite the image into 221 00:11:48.309 --> 00:11:51.080 what they, um, black hole look like. And it turned 222 00:11:51.129 --> 00:11:55.139 out looked exactly like the one in interstellar, uh, which, which, uh, 223 00:11:55.220 --> 00:11:57.179 there's a good reason for that. Uh, Christopher Nolan hired 224 00:11:57.200 --> 00:12:01.009 a Caltech physicist named Kim Thorne, who actually figured out 225 00:12:01.070 --> 00:12:04.259 what it should look like. And, uh, the, EHT actually 226 00:12:04.299 --> 00:12:04.960 validated that. 227 00:12:05.120 --> 00:12:07.659 And it was very low resolution, if I remember correctly. 228 00:12:07.759 --> 00:12:10.259 Of course. But, you know, you're literally talking billions of 229 00:12:10.299 --> 00:12:12.620 light years away. So it's a miracle it works at all. 230 00:12:12.639 --> 00:12:15.840 But it's just, you know, we're getting new superpowers. In May, 231 00:12:15.860 --> 00:12:19.519 SpaceX launches the very first batch of Starlink satellites, an 232 00:12:19.559 --> 00:12:23.850 array of 60. Yeah. In August, SpaceX does their first 233 00:12:23.879 --> 00:12:27.230 flight of Starhopper. This was a funny little looking can 234 00:12:27.269 --> 00:12:29.590 of a thing with some legs on it. Flew just 235 00:12:29.629 --> 00:12:33.309 a short distance and landed again. It's the beginning of Starship, 236 00:12:33.500 --> 00:12:35.580 but the really important thing is this is their new 237 00:12:35.679 --> 00:12:39.679 Raptor engine, a methane liquid oxygen engine. And it's also 238 00:12:39.759 --> 00:12:41.620 full flow combustion. So that was the first time that 239 00:12:41.659 --> 00:12:44.840 a full flow combustion stage combustion engine had ever flown. 240 00:12:45.399 --> 00:12:47.889 And it'll get bigger for that. And one little piece 241 00:12:47.929 --> 00:12:51.809 of additional Boeing news alongside killing people in their dangerous 737, 242 00:12:51.809 --> 00:12:53.049 which admittedly is now fixed. 243 00:12:53.090 --> 00:12:53.309 Yeah. 244 00:12:53.370 --> 00:12:56.149 And I have flown on it. Uh, Boeing flies their 245 00:12:56.190 --> 00:12:58.570 Starliner to the International Space Station for the first time, 246 00:12:58.649 --> 00:13:00.190 except for that part where it never got to the 247 00:13:00.230 --> 00:13:00.889 space station. 248 00:13:01.190 --> 00:13:01.529 Right. 249 00:13:02.529 --> 00:13:07.529 Software bugs in the system cause the vehicle to decide 250 00:13:07.580 --> 00:13:09.799 that it's actually farther along the mission than it actually is. 251 00:13:09.860 --> 00:13:13.580 And it tries to correct its orientation inappropriately. And before 252 00:13:13.600 --> 00:13:16.039 they can send commands to get it to stop doing that, 253 00:13:16.500 --> 00:13:18.980 it burns

up so much of its maneuvering fuel. That 254 00:13:19.000 --> 00:13:20.620 it's unable to make it to the space station. They 255 00:13:20.679 --> 00:13:23.419 do get control of it, fix the problem with the 256 00:13:23.460 --> 00:13:27.710 software and successfully de-orbit and recover the vehicle. But that 257 00:13:27.730 --> 00:13:29.490 will only be the beginning of a whole series of 258 00:13:29.529 --> 00:13:32.909 terrible problems for Starliner that are not resolved to this day. 259 00:13:33.190 --> 00:13:36.230 Hey, when you mentioned Starlink, you were using Starlink, right? 260 00:13:36.450 --> 00:13:37.070 Are you using it now? 261 00:13:37.269 --> 00:13:40.149 I wasn't at that point. It would be later. I 262 00:13:40.169 --> 00:13:42.090 would apply for the beta and get into the beta 263 00:13:42.269 --> 00:13:43.909 in a couple of years after that. But are you 264 00:13:43.929 --> 00:13:47.549 using it right now? I'm not right now, no. It's 265 00:13:47.600 --> 00:13:49.940 my backup. I have fiber now to this house in 266 00:13:49.960 --> 00:13:52.820 the middle of nowhere, which is ridiculous. It is ridiculous. 267 00:13:52.840 --> 00:13:56.360 Starlink is the backup. Okay, onto the computing side of things. 268 00:13:56.460 --> 00:13:59.940 A whole bunch of stories around OpenAI. So February of 269 00:13:59.940 --> 00:14:04.940 2019 is the release of GPT-2. And remember that the 270 00:14:05.340 --> 00:14:07.649 mantra of OpenAI had been to do AI out in 271 00:14:07.659 --> 00:14:09.690 the open, do it also open source, right? That's why 272 00:14:09.710 --> 00:14:13.350 it's called OpenAI. But they come to the conclusion that 273 00:14:13.370 --> 00:14:16.809 their largest model in GPT-2, which was a 1.5 billion 274 00:14:16.830 --> 00:14:20.379 parameter model, oh, how quaint, is too powerful and that 275 00:14:20.389 --> 00:14:22.460 it shouldn't be shared publicly. So they only release a 276 00:14:22.480 --> 00:14:26.000 very tiny version of it just to show its potential. 277 00:14:26.740 --> 00:14:29.019 And they are starting to reconsider what the company's all about. 278 00:14:29.720 --> 00:14:31.860 Part of this is they're working on a paper, which 279 00:14:31.879 --> 00:14:36.700 they'll publish in 2020, about... the scale necessary to build 280 00:14:36.720 --> 00:14:39.639 these language models and that being a not-for-profit is just 281 00:14:39.679 --> 00:14:42.240 not feasible. It's not the way they're going to be successful. 282 00:14:42.620 --> 00:14:44.909 And so in March, they'll restructure OpenAI to become what 283 00:14:44.929 --> 00:14:48.009 they call a capped profit company, which is funny because 284 00:14:48.029 --> 00:14:49.830 this is all around the time that likely they're talking 285 00:14:49.870 --> 00:14:54.269 to Microsoft because in June, Kevin Scott wrote an email 286 00:14:54.370 --> 00:14:58.679 to Bill Gates and Satya Nadella called Thoughts on OpenAI. 287 00:14:59.490 --> 00:15:02.190 where

he talked about the fact that OpenAI and DeepMind 288 00:15:02.210 --> 00:15:05.110 and Google Brain were well ahead of Microsoft and that 289 00:15:05.129 --> 00:15:09.490 there was an opportunity to invest in OpenAI and put 290 00:15:09.509 --> 00:15:12.169 them over onto Azure and maybe have a relationship. That, 291 00:15:12.210 --> 00:15:15.379 of course, will happen in July. Sam Altman and Nadella 292 00:15:15.389 --> 00:15:19.659 will be on stage together. We'll announce an exclusive cloud partnership. 293 00:15:19.720 --> 00:15:20.539 I do remember that. 294 00:15:20.879 --> 00:15:23.740 And finally, in December, Microsoft will put a billion dollars 295 00:15:23.879 --> 00:15:27.460 into OpenAI, although how much of that they'll spend buying Azure, 296 00:15:27.480 --> 00:15:31.340 we don't really know. Related to one of your stories 297 00:15:31.399 --> 00:15:35.500 early on about China, in March, the UK publishes a 298 00:15:35.539 --> 00:15:41.429 report about Huawei, concerns about Chinese security with kill switches 299 00:15:41.549 --> 00:15:45.049 on 5G networking and things like that. The UK has 300 00:15:45.110 --> 00:15:48.169 a group that's actually getting into the software that drives 301 00:15:48.230 --> 00:15:50.629 all of those things, but they consider the software such 302 00:15:50.720 --> 00:15:54.179 poor quality that they can't even verify its reliability or 303 00:15:54.220 --> 00:15:59.559 security and consider it unsafe to use. That will result 304 00:15:59.580 --> 00:16:03.360 in May, the Trump administration will literally say, you can't 305 00:16:03.580 --> 00:16:06.899 use Huawei stuff, full stop. And it'll spread around all 306 00:16:06.919 --> 00:16:09.419 of the Western world, really. That's around the time the 307 00:16:09.460 --> 00:16:12.370 first 5G networks actually get deployed in the US, in April. 308 00:16:13.429 --> 00:16:16.450 Also in April, but on April 2nd, not April 1st, 309 00:16:16.669 --> 00:16:21.129 probably deliberately, Google shuts down, Google +. Can't do that 310 00:16:21.169 --> 00:16:26.700 on April 2nd, it's not funny. Okay, September, Visual Studio 2019. 311 00:16:26.700 --> 00:16:31.470 with Framework 4.8, but also. NET Core 3.0, which is 312 00:16:31.529 --> 00:16:34.379 really the point where you kind of hit parity, so 313 00:16:34.409 --> 00:16:37.519 the features, In the old framework that we wanted in 314 00:16:37.539 --> 00:16:39.799 the open source cloud platform version, they were all there 315 00:16:39.879 --> 00:16:41.240 now and more or less complete. 316 00:16:41.299 --> 00:16:42.519 That's where I started using it. 317 00:16:42.559 --> 00:16:42.840 Yeah. 318 00:16:42.919 --> 00:16:44.320 I started using it at three. 319 00:16:44.519 --> 00:16:46.080 Yeah, and it was the point where it's like, hey, 320 00:16:46.100 --> 00:16:48.000 this is the end of the road. There won't be a. 321 00:16:48.139 --> 00:16:50.299 NET Core 4. There won't be two versions of. NET 322 00:16:50.350 --> 00:16:52.470 after this. There'll just be five, although you know the 323 00:16:52.509 --> 00:16:56.210 old framework, 4.8 will never go anymore. And in December, 324 00:16:56.230 --> 00:16:59.669 they'll put out 3.1, fixing some of the problems. Two 325 00:16:59.690 --> 00:17:04.309 more stories. October. Google's Sycamore processor. So the first real 326 00:17:04.430 --> 00:17:09.130 public demonstration of what we would call quantum supremacy. This 327 00:17:09.190 --> 00:17:12.170 was one of those chandeliers soaked in liquid helium style 328 00:17:12.230 --> 00:17:15.259 quantum computers, very fragile. It had 54 qubits, only 53 329 00:17:15.259 --> 00:17:19.220 of them were functioning, did a 200 second run doing 330 00:17:19.259 --> 00:17:23.180 a random number sampling task. Google argued that this would 331 00:17:23.200 --> 00:17:25.819 take 10,000 years with a traditional computer and they finished 332 00:17:25.839 --> 00:17:28.619 it in 200 seconds. IBM, of course, challenged the numbers 333 00:17:28.640 --> 00:17:32.519 and then demonstrated various strata on quantum strategies to get 334 00:17:32.619 --> 00:17:34.650 pretty good results. I think they're fastest when they got 335 00:17:34.670 --> 00:17:39.130 it down to a couple of days, but whatever. But 336 00:17:39.170 --> 00:17:42.980 it is in a wave of advancement in quantum computing. 337 00:17:43.559 --> 00:17:45.160 And last but not least, because I do think it 338 00:17:45.220 --> 00:17:47.799 impacts a lot of the conversations we're having today in 339 00:17:47.819 --> 00:17:54.180 December at Amazon's reInvent conference, They talk about Graviton2, which 340 00:17:54.240 --> 00:17:59.519 was custom ARM processors for workloads in EC2. They're promising 341 00:17:59.519 --> 00:18:02.519 40% better price performance. Up until this point, for the 342 00:18:02.579 --> 00:18:07.809 most part, the cloud had been regular machines bought with 343 00:18:07.890 --> 00:18:10.109 Intel and AMD chips and so forth, bought by the 344 00:18:10.150 --> 00:18:12.910 big vendors, already pre-racked and so forth. But now the 345 00:18:12.930 --> 00:18:15.910 cloud companies, Amazon being one, but also Microsoft and Google 346 00:18:15.930 --> 00:18:18.319 as well. Google was already going into their TensorFlows and 347 00:18:18.339 --> 00:18:21.450 things like that. Are starting to build their own hardware 348 00:18:21.470 --> 00:18:24.349 to optimize for cloud workloads. And that's going to change 349 00:18:24.410 --> 00:18:25.329 things going forward. 350 00:18:25.529 --> 00:18:25.769 Yeah. 351 00:18:25.970 --> 00:18:26.950 Those are my stories, friend. 352 00:18:27.170 --> 00:18:30.740 All right. Well, that brings us to better know a framework. 353 00:18:30.859 --> 00:18:31.339 Awesome. 354 00:18:31.660 --> 00:18:33.819 Or something. Better Know Something, maybe we should call it. 355 00:18:33.829 --> 00:18:35.009 Better Know Something. 356 00:18:35.250 --> 00:18:36.369

That would have been a great title. 357 00:18:37.410 --> 00:18:47.670 All right, man, what do you got? Okay, so for 358 00:18:47.710 --> 00:18:51.170 those of you paying attention to my other shows, Rocky 359 00:18:51.210 --> 00:18:55.180 Latka and I started with him as co-host on Code 360 00:18:55.200 --> 00:18:59.180 It With AI, which is presented by DevExpress. 361 00:19:00.180 --> 00:19:00.480 And we.... 362 00:19:02.000 --> 00:19:08.200 Just put Quen 3.8 local to the test. Quen 3.8 363 00:19:08.200 --> 00:19:11.380 is a model, and I ran it on Ollama. And 364 00:19:11.779 --> 00:19:15.200 we had done on episodes 29 and 30 with Jeff Fritz, 365 00:19:15.740 --> 00:19:20.420 we had done comparisons between local models running in this 366 00:19:20.519 --> 00:19:22.480 hardware that I have, right, in Ollama. 367 00:19:22.859 --> 00:19:23.019 Yeah. 368 00:19:23.240 --> 00:19:26.869 And Quen 3.6 was the winner by far. So I 369 00:19:27.029 --> 00:19:28.890 was thinking Quen 3.8, going to be great. 370 00:19:30.269 --> 00:19:30.509 Yeah. 371 00:19:31.269 --> 00:19:43.950 Not so much. Interesting. because Alama allocates context depending on 372 00:19:43.970 --> 00:19:46.420 the amount of VRAM you have. 373 00:19:47.599 --> 00:19:52.420 So I got 30, 35 or 32, 32 K based 374 00:19:52.480 --> 00:19:54.259 on the amount of VRAM that I had, but I 375 00:19:54.279 --> 00:19:57.440 don't think it was enough because it was, it was 376 00:19:57.849 --> 00:20:01.029 doing the confusing things that the other models had done earlier, 377 00:20:01.329 --> 00:20:04.569 which is telling you that it, you know, couldn't reach 378 00:20:04.589 --> 00:20:10.569 the API, giving you some weird nil error, and stopping. 379 00:20:11.809 --> 00:20:18.650 So Rocky tells me about llama.cpp. And llama.cpp is an 380 00:20:18.710 --> 00:20:24.250 alternative to Ollama that it allows you to host models. 381 00:20:24.329 --> 00:20:27.430 But the cool thing about it is that it can 382 00:20:27.490 --> 00:20:30.890 take the compute heavy stuff and run that in VRAM. 383 00:20:31.309 --> 00:20:33.470 And then it can use your system RAM for the 384 00:20:33.509 --> 00:20:35.299 rest of it. Now, I don't know if it swaps 385 00:20:35.359 --> 00:20:39.309 things in and out, system RAM, VRAM, or it just 386 00:20:39.549 --> 00:20:42.990 runs some things that don't require such a heavy load 387 00:20:45.490 --> 00:20:49.609 in system RAM, but that's it. So then there are 388 00:20:49.650 --> 00:20:52.630 only certain models that can run, but there's a QEN 389 00:20:52.670 --> 00:20:57.279 model that runs that's bigger that I'm going to try 390 00:20:57.359 --> 00:21:01.160 for next week's Code with AI. Well, I say next week. 391 00:21:01.859 --> 00:21:07.940 We're recording this on August 21st. or 20th, rather. 392 00:21:09.500 --> 00:21:09.900 I'm sorry. 393 00:21:10.299 --> 00:21:15.640 We're recording this on August 21st, and it won't come 394 00:21:15.680 --> 00:21:20.700 out until September 10th. So the episode would be 43, 395 00:21:20.700 --> 00:21:25.309 and that would be on last week, September 2nd. So 396 00:21:25.329 --> 00:21:27.140 if you want to see what that does, I'm going 397 00:21:27.160 --> 00:21:29.130 to have a live demo of it. I'm going to 398 00:21:29.150 --> 00:21:32.269 try it, but llama.cpp. Know it, learn it, love it. 399 00:21:32.829 --> 00:21:34.029 Who's talking to us today, Richard? 400 00:21:34.490 --> 00:21:37.130 I had to go back. We're doing mathematics today, so 401 00:21:37.150 --> 00:21:38.509 I had to go back to a mathematics show. So, 402 00:21:38.529 --> 00:21:41.990 I went way back. 1252, which is from 2016. Our 403 00:21:42.019 --> 00:21:48.940 friend Seth Juarez talking about his library, NUML. Because secretly, 404 00:21:49.460 --> 00:21:51.599 Seth Juarez, as charming and entertaining as he was on 405 00:21:51.640 --> 00:21:54.609 Channel 9, actually a maths guy. Got a real, you know, 406 00:21:54.619 --> 00:21:58.009 got a master's degree. Super smart, you know. Great at 407 00:21:58.049 --> 00:21:59.470 explaining the whole. 408 00:21:59.769 --> 00:22:00.029 Oh, yeah. 409 00:22:00.650 --> 00:22:02.650 LLM wave too. We've done some cool shows with it. 410 00:22:03.269 --> 00:22:06.789 So this is a comment from, uh, Kirian O'Neill, who 411 00:22:06.829 --> 00:22:09.839 says another scheduling library along the lines of courts.net. We 412 00:22:09.880 --> 00:22:12.460 were talking about that library as well. Worth mentioning is 413 00:22:12.599 --> 00:22:15.839 hang fire. The advantage I've gained from using hang fires 414 00:22:15.880 --> 00:22:18.180 that it runs in process. It doesn't require a separate 415 00:22:18.240 --> 00:22:20.849 window service. And depending on your use cases can be 416 00:22:20.869 --> 00:22:23.279 a big advantage. And it's one less thing to think 417 00:22:23.339 --> 00:22:26.740 about when deploying because, yeah, pushing out stuff to count 418 00:22:26.779 --> 00:22:29.880 on Windows services and stuff is ugly if you're going 419 00:22:29.900 --> 00:22:31.720 to try and make things work properly for you. But, 420 00:22:32.299 --> 00:22:33.960 you know, this was a whole conversation we had with 421 00:22:34.009 --> 00:22:36.930 Seth about how you do these long compute workloads when 422 00:22:36.950 --> 00:22:39.150 you're working out things like machine learning models and so 423 00:22:39.190 --> 00:22:41.009 forth where they may run for a couple of days. 424 00:22:41.630 --> 00:22:43.450 And you don't want to just tie up the whole machine. 425 00:22:43.490 --> 00:22:45.630 You want to run them in the background. Yep. So, Kirian, 426 00:22:45.650 --> 00:22:47.450 thank you so much for your comment. And a copy 427 00:22:47.470 --> 00:22:48.849 of Music to Code By is on its way to you. 428 00:22:48.869 --> 00:22:50.430 And if you'd like a copy of Music to Code By, 429 00:22:50.450 --> 00:22:53.460 write a comment on the website at. netrocks. com or on

430 00:22:53.480 --> 00:22:55.019 the Facebooks. We publish every show there. And if you 431 00:22:55.059 --> 00:22:56.640 comment there and I read it in the show, we'll 432 00:22:56.660 --> 00:22:57.740 send you a copy of Music to Code By. 433 00:22:57.819 --> 00:22:59.180 And if you want to just go get Music to 434 00:22:59.200 --> 00:23:01.099 Code By, it's at musictocodeby.net. 435 00:23:01.980 --> 00:23:02.180 All right. 436 00:23:02.200 --> 00:23:05.160 We've taken up so much time with this intro stuff. 437 00:23:05.299 --> 00:23:07.099 I think we ought to take our break now so 438 00:23:07.119 --> 00:23:11.039 we can have an uninterrupted talk with Jeffrey Sachs. So 439 00:23:11.059 --> 00:23:17.369 we'll be right back after these very important messages. And 440 00:23:17.390 --> 00:23:21.109 we're back. It's. NET Rocks. I'm Carl Franklin. That's Richard Campbell. 441 00:23:21.349 --> 00:23:21.529 Hey. 442 00:23:21.789 --> 00:23:24.309 And also here with us is Jeffrey Sachs. 443 00:23:24.430 --> 00:23:25.250 Hi. Hi. 444 00:23:26.109 --> 00:23:30.279 Jeffrey Sachs is the founder and sole developer of Numerics.net, 445 00:23:30.910 --> 00:23:32.980 a set of numerical computing libraries for. 446 00:23:33.200 --> 00:23:33.359 NET. 447 00:23:34.059 --> 00:23:37.480 He has been building the library since 2005 when the 448 00:23:37.539 --> 00:23:42.130 first version was released for. NET 1.1. Over the years, Numerics.net 449 00:23:42.170 --> 00:23:46.089 has been used for applications ranging from calculating radiation doses 450 00:23:46.170 --> 00:23:50.650 for cancer treatment and developing truck braking systems to building 451 00:23:50.690 --> 00:23:56.319 support software for atomic force microscopes. Jeffrey's work on numerical 452 00:23:56.380 --> 00:23:57.680 software predates. 453 00:23:57.960 --> 00:23:58.160 NET. 454 00:23:58.380 --> 00:23:59.619 Jeffrey, welcome. 455 00:23:59.859 --> 00:24:00.119 Hi. 456 00:24:00.779 --> 00:24:02.180 Thank you. Thanks for having me. 457 00:24:02.460 --> 00:24:03.029 You're welcome. 458 00:24:03.490 --> 00:24:07.200 Sorry about the long intro. If you're okay with it, 459 00:24:07.230 --> 00:24:10.299 we can go a little longer today. But my first 460 00:24:10.359 --> 00:24:14.259 question is, what is numerical computing? 461 00:24:14.740 --> 00:24:19.799 I would say numerical computing is the task of computing 462 00:24:19.859 --> 00:24:28.150 values to a requested accuracy with limited precision. And do 463 00:24:28.190 --> 00:24:30.210 that as fast as possible. 464 00:24:30.450 --> 00:24:36.410 So it's basically just math equations in code. Essentially, like 465 00:24:36.549 --> 00:24:39.150 a MATLAB kind of thing? 466 00:24:39.730 --> 00:24:41.069 Yeah, that's what it comes down to. 467 00:24:41.309 --> 00:24:42.730 Simulink, yeah. 468 00:24:43.019 --> 00:24:45.799 So this is outside the spectrum of what the built-in 469 00:24:45.839 --> 00:24:50.220 mathematical functions in. NET could do? 470 00:24:50.579 --> 00:24:52.119 Yes, way beyond, actually. 471 00:24:52.319 --> 00:24:52.579 Right. 472 00:24:54.319 --> 00:24:59.589 Vectors, matrices, probability, and statistics, all kinds of fun stuff. 473 00:24:59.769 --> 00:25:01.789 So it's all based on the fundamental stuff that's in 474 00:25:01.809 --> 00:25:04.970 the framework, but then you do these... abstractions on top 475 00:25:05.029 --> 00:25:07.269 of it that give you the higher level. 476 00:25:08.289 --> 00:25:08.710 That's right. 477 00:25:09.230 --> 00:25:10.710 Yeah, constructs. 478 00:25:10.990 --> 00:25:13.119 All right, let's dust off our math chop, see if 479 00:25:13.130 --> 00:25:19.019 we remember any of this stuff from school. Holy man. So, 480 00:25:19.140 --> 00:25:20.940 I mean, just in your comment alone, you were talking 481 00:25:20.960 --> 00:25:23.680 about things like radiation doses. So, can you talk a 482 00:25:23.680 --> 00:25:26.240 bit about what kind of math we need there? It's 483 00:25:26.279 --> 00:25:27.500 a great thing to figure out. 484 00:25:27.799 --> 00:25:28.680 Actually, I'm not sure. 485 00:25:28.700 --> 00:25:29.140 I just. 486 00:25:29.740 --> 00:25:31.339 hear a lot of stories from customers. 487 00:25:31.759 --> 00:25:32.119 Oh, right. 488 00:25:32.460 --> 00:25:35.019 Um, these are just your customers doing cool things with 489 00:25:35.059 --> 00:25:35.720 your software. 490 00:25:35.880 --> 00:25:36.140 Yeah. 491 00:25:36.619 --> 00:25:38.440 So that's the most fun part of what I do. 492 00:25:38.519 --> 00:25:39.940 I hear all sorts of things. 493 00:25:40.160 --> 00:25:40.789 Yeah. Yeah. 494 00:25:41.210 --> 00:25:43.190 Um, and you heard some variety of what I hear. 495 00:25:43.430 --> 00:25:45.509 Your background is in mathematics then? 496 00:25:45.650 --> 00:25:47.950 Yes, it is. I actually, right. 497 00:25:48.190 --> 00:25:49.990 So you just take him what you've learned and said like, 498 00:25:50.089 --> 00:25:52.190 how could I do these things in.net? 499 00:25:52.539 --> 00:25:55.799 Yes. I, I've been doing this pretty much my whole 500 00:25:55.839 --> 00:25:58.259 life ever since I got my hands on the computer. 501 00:25:59.000 --> 00:26:02.329 Um, And then went to university. 502 00:26:02.890 --> 00:26:06.339 Got a degree in computing science, so specializing in the 503 00:26:06.440 --> 00:26:07.220 numerical stuff. 504 00:26:07.660 --> 00:26:08.259 And then. 505 00:26:09.900 --> 00:26:13.339 After some time of building things privately, like just for 506 00:26:13.380 --> 00:26:16.940 my own enjoyment, I thought, well, why not turn this 507 00:26:17.019 --> 00:26:21.079 into my job and do it professionally? 508 00:26:21.460 --> 00:26:21.680 Wow. 509 00:26:21.880 --> 00:26:23.890 And that's how Numerics.net got started. 510 00:26:24.269 --> 00:26:24.450 Wow. 511 00:26:24.940 --> 00:26:28.119 You remind me of a product that when I was 512 00:26:28.160 --> 00:26:31.460 at Crescent Software, we sold. I didn't write it. I

513 00:26:32.130 --> 00:26:35.730 just did tech support. But it was called QuickPack Scientific. 514 00:26:36.829 --> 00:26:41.859 And so in that was a bunch of assembly language things, 515 00:26:42.460 --> 00:26:45.759 calls that you could call from basic, from QuickBasic, Basic 516 00:26:45.759 --> 00:26:50.269 7 PDS, and even Visual Basic, that did all these 517 00:26:50.329 --> 00:26:53.349 kinds of things. And I wondered even back then, why 518 00:26:53.369 --> 00:26:55.150 do you need all this if you have the fundamentals? 519 00:26:55.210 --> 00:26:56.970 And it's kind of like, you know, why do you 520 00:26:56.990 --> 00:26:59.210 need a database if you can open and read and 521 00:26:59.230 --> 00:26:59.789 write files? 522 00:27:00.890 --> 00:27:01.650 Right? 523 00:27:02.069 --> 00:27:06.650 These are layers of abstraction that help you as a non-programmer, 524 00:27:06.950 --> 00:27:11.359 maybe a scientist that dabbles in programming, do stuff easily. 525 00:27:11.539 --> 00:27:15.099 Well, it's not just about the layers of abstraction, although 526 00:27:15.119 --> 00:27:20.289 that can be useful as well. It's also about the 527 00:27:20.329 --> 00:27:25.029 limitations that you have doing math on a computer and 528 00:27:25.109 --> 00:27:26.309 still doing things correctly. 529 00:27:26.579 --> 00:27:26.859 Yeah. 530 00:27:26.950 --> 00:27:29.319 So I said, it's, we got to dig into this 531 00:27:29.380 --> 00:27:32.420 because I think it's fascinating. What, what are the, we never, 532 00:27:32.700 --> 00:27:34.319 most of the time we don't bump into these limitations. 533 00:27:34.519 --> 00:27:35.759 What are the limitations? 534 00:27:35.980 --> 00:27:41.380 Well, the primary limitation is you can't represent every number 535 00:27:41.640 --> 00:27:43.710 from real life in a computer system. 536 00:27:43.910 --> 00:27:44.190 Right. 537 00:27:44.369 --> 00:27:44.569 Right. 538 00:27:44.710 --> 00:27:48.549 So we have, integers, and then we have what we 539 00:27:48.589 --> 00:27:52.970 call real numbers. But those are really the double precision 540 00:27:53.049 --> 00:27:55.529 floating point numbers is the official name. Right. 541 00:27:55.670 --> 00:27:58.190 Yeah. And I think the floating point's a better term 542 00:27:58.230 --> 00:28:01.009 just because it lets you know. This is only so accurate. 543 00:28:01.269 --> 00:28:01.710 Yeah. 544 00:28:01.950 --> 00:28:08.670 So the limitation is these numbers have a very specific format. 545 00:28:09.210 --> 00:28:11.309 They're an integer times a power of two. 546 00:28:12.009 --> 00:28:12.230 Right. 547 00:28:12.529 --> 00:28:15.109 And you only have a certain range to work with. 548 00:28:15.720 --> 00:28:21.039 So every calculation you do, you basically are able to 549 00:28:21.180 --> 00:28:23.039 use only those numbers. Yeah. 550 00:28:23.160 --> 00:28:24.319 And that's what makes it hard. 551 00:28:24.759 --> 00:28:28.119 Right, right. So it's the precision. And you mentioned precision 552 00:28:28.420 --> 00:28:32.710 in your definition of numerical computing, that you may want 553 00:28:33.089 --> 00:28:38.450 less or more. But I get more. Why less? Yeah. 554 00:28:38.849 --> 00:28:44.630 Well, in modern-day computing, there's a lot of talk about– 555 00:28:45.359 --> 00:28:49.440 reducing the number of bits required for LLMs and so 556 00:28:49.500 --> 00:28:53.920 forth to do their calculations and still have good results. 557 00:28:54.539 --> 00:28:58.769 So they'll sample down from the original 16 or 32 558 00:28:58.769 --> 00:29:02.309 bits down to sometimes as little as four or two 559 00:29:02.349 --> 00:29:02.910 bits even. 560 00:29:03.170 --> 00:29:03.450 Wow. 561 00:29:03.670 --> 00:29:07.670 So that's why you would use less. In general, for calculations, 562 00:29:09.569 --> 00:29:13.750 you would use the standard four or eight number formats. 563 00:29:15.150 --> 00:29:19.269 because the resources aren't as tight and the computation isn't 564 00:29:19.849 --> 00:29:20.470 as intense. 565 00:29:20.809 --> 00:29:21.450 Yeah, okay. 566 00:29:21.630 --> 00:29:24.890 And so the point being, when you use a higher precision, 567 00:29:24.950 --> 00:29:27.109 it's just going to take longer for no value. 568 00:29:27.390 --> 00:29:30.609 Yeah, but if you use too little precision, things can 569 00:29:30.650 --> 00:29:31.890 go terribly long as well. 570 00:29:32.130 --> 00:29:32.369 Right. 571 00:29:32.769 --> 00:29:37.549 There's a famous example of um an arianne 5 rocket 572 00:29:38.839 --> 00:29:40.220 in 96 i think. 573 00:29:40.099 --> 00:29:42.700 It was oh yeah they lost the first one they. 574 00:29:42.579 --> 00:29:49.140 Lost the first one because some value was um stored 575 00:29:49.339 --> 00:29:54.240 as a 16-bit value for the arianne 4 rocket the 576 00:29:54.279 --> 00:29:58.339 predecessor right and they converted down from 64 bits to 577 00:29:58.339 --> 00:30:02.809 16 got an overflow which sent their navigation system into 578 00:30:02.930 --> 00:30:06.259 some kind of error state and they had to terminate 579 00:30:06.539 --> 00:30:07.680 the launch. 580 00:30:07.900 --> 00:30:10.140 Yeah, that's a very expensive boo-boo. 581 00:30:10.220 --> 00:30:10.799 Yes, it is. 582 00:30:10.880 --> 00:30:12.640 Like billion-dollar boo-boo. 583 00:30:12.940 --> 00:30:16.440 Yeah, and so one of the things that makes it 584 00:30:16.480 --> 00:30:21.220 hard is because you have that limited set of numbers, 585 00:30:23.329 --> 00:30:26.349 whenever you do a calculation, you have to start by 586 00:30:27.190 --> 00:30:32.059 approximating the number you get from real life by a 587 00:30:32.200 --> 00:30:34.220 number that's in your set that you can work with. 588 00:30:35.480 --> 00:30:38.460 So you have to round it off and that already 589 00:30:38.720 --> 00:30:42.900 right off, right out of the gate, you start with 590 00:30:42.940 --> 00:30:48.740 an error and then errors propagate. Like

every calculation you do, 591 00:30:48.759 --> 00:30:52.900 when you add two numbers, the sum of those two 592 00:30:52.940 --> 00:30:58.400 numbers may not be a floating point number again. So 593 00:30:58.420 --> 00:31:03.700 then you get additional errors And sometimes it can explode and, well, 594 00:31:04.019 --> 00:31:04.900 lead to explosions. 595 00:31:05.460 --> 00:31:07.259 Right. Quite literally. 596 00:31:07.500 --> 00:31:07.720 Yeah. 597 00:31:07.880 --> 00:31:10.559 Yeah, I remember watching that, actually. And it's like suddenly 598 00:31:10.599 --> 00:31:12.779 the engines were trying to move the rocket in ways 599 00:31:12.859 --> 00:31:14.400 it really wouldn't want to move. And then it just 600 00:31:14.420 --> 00:31:15.599 sort of broke into pieces. 601 00:31:15.839 --> 00:31:16.599 Yeah, that's right. 602 00:31:16.819 --> 00:31:19.440 I had a friend. He's gone now. But he was 603 00:31:19.740 --> 00:31:27.049 a professor of mathematics. And he called himself a philosopher 604 00:31:27.480 --> 00:31:27.940 of math. 605 00:31:28.710 --> 00:31:28.950 And I. 606 00:31:30.650 --> 00:31:34.470 Was, I guess, into things that were so abstract that 607 00:31:35.150 --> 00:31:38.150 nobody could understand them, and you had to just think 608 00:31:38.210 --> 00:31:42.089 about them completely differently. One of those things that I 609 00:31:42.150 --> 00:31:47.670 think of in that vein are imaginary numbers. What the 610 00:31:47.710 --> 00:31:49.490 hell is an imaginary number? 611 00:31:50.779 --> 00:31:51.039 Right? 612 00:31:51.410 --> 00:31:55.880 Well, an imaginary number is a trick, basically, to. 613 00:31:57.759 --> 00:32:01.859 Make... the math work. So there's. 614 00:32:03.880 --> 00:32:07.880 A theory where when you compute the roots of a 615 00:32:07.920 --> 00:32:17.839 quadratic equation, you always have two roots. If you have 616 00:32:17.859 --> 00:32:21.119 real numbers as roots, that's not always the case. But 617 00:32:21.180 --> 00:32:25.809 if you allow this extension by using the square root 618 00:32:25.920 --> 00:32:32.390 of minus one as another dimension, then you can always 619 00:32:32.430 --> 00:32:36.150 get two roots. And so there's all kinds of lovely, 620 00:32:36.190 --> 00:32:40.859 beautiful math that just falls into place perfectly when you 621 00:32:40.880 --> 00:32:41.210 do that. 622 00:32:41.690 --> 00:32:42.559 I still don't get it. 623 00:32:42.900 --> 00:32:44.700 I'm remembering enough of this stuff to realize, as soon 624 00:32:44.720 --> 00:32:46.980 as you said imaginary numbers, like square root of negative two, 625 00:32:47.500 --> 00:32:50.240 that shouldn't be possible, but there's a fix for it. 626 00:32:50.440 --> 00:32:55.119 Yeah. So it's not purely mathematical. It's actually some, like 627 00:32:55.440 --> 00:32:58.019 most of quantum physics is also expressed in quantum, in, uh, 628 00:32:58.470 --> 00:33:02.400 in terms of complex numbers. So, how real that is 629 00:33:02.460 --> 00:33:05.539 is also questionable, but that's a different discussion. 630 00:33:06.660 --> 00:33:08.819 Well, you know, God doesn't play dice with the universe. 631 00:33:10.220 --> 00:33:12.650 Would you consider yourself a philosopher of math? 632 00:33:12.869 --> 00:33:14.089 A little bit, but not too much. 633 00:33:14.569 --> 00:33:19.190 Not the philosopher king, just a philosopher. No. 634 00:33:20.890 --> 00:33:25.720 The pure math and the computer math are actually very different. 635 00:33:26.089 --> 00:33:27.329 It's a very different story. 636 00:33:27.430 --> 00:33:28.609 Oh, sure, yeah. 637 00:33:28.750 --> 00:33:33.059 You don't get into extreme abstractions that only a handful 638 00:33:33.079 --> 00:33:34.299 of people understand. 639 00:33:35.240 --> 00:33:38.299 But as I understand it, mathematics and computing in general 640 00:33:38.380 --> 00:33:41.440 has been a series of compromises based on the limitations 641 00:33:42.160 --> 00:33:43.660 of the hardware available at the time. 642 00:33:44.000 --> 00:33:44.660 Yes, that's right. 643 00:33:45.009 --> 00:33:45.589 And the language. 644 00:33:46.490 --> 00:33:52.289 Language, too. There's actually funny stories about Fortran, the first 645 00:33:52.349 --> 00:34:00.420 programming language, which has... Originally, it didn't have if statements. 646 00:34:00.640 --> 00:34:04.059 It had a conditional jump. It didn't have. 647 00:34:06.910 --> 00:34:12.449 The logical operators and the comparison operators are written out 648 00:34:12.789 --> 00:34:16.570 with dots. Dot, L, T, dot is less than. The 649 00:34:16.590 --> 00:34:21.469 reason they did that was because at the time... computers 650 00:34:21.510 --> 00:34:23.449 didn't have less than signs. 651 00:34:23.829 --> 00:34:26.530 Right. The ASCII set hadn't been done yet. 652 00:34:26.690 --> 00:34:27.130 That's right. 653 00:34:27.389 --> 00:34:27.650 Wow. 654 00:34:27.829 --> 00:34:28.670 Was it EPSIDIC? 655 00:34:29.670 --> 00:34:30.789 Even earlier. 656 00:34:30.869 --> 00:34:36.070 Another interesting thing about Fortran, white space doesn't matter at all. 657 00:34:36.349 --> 00:34:36.630 Right. 658 00:34:36.869 --> 00:34:39.170 You can put spaces anywhere in the middle of a name, 659 00:34:39.190 --> 00:34:45.030 of a variable, anywhere. The reason they did that is 660 00:34:45.110 --> 00:34:52.179 because back in the day, people wrote their programs on 661 00:34:52.300 --> 00:34:57.090 punch cards and there were punch card operators who translated 662 00:34:57.110 --> 00:35:04.809 or like who entered the text in punch cards, did 663 00:35:04.829 --> 00:35:11.139 the punching to then feed into the computers. And what 664 00:35:11.179 --> 00:35:15.099 they found was that they were very sloppy with spaces 665 00:35:15.460 --> 00:35:18.500 in the transcriptions. And so there were lots of errors 666 00:35:19.340 --> 00:35:24.539 because spaces were at the time significant. And so they 667 00:35:24.559

--> 00:35:27.440 did away with that so that their programs could actually run. 668 00:35:27.920 --> 00:35:28.719 It's a workaround. 669 00:35:28.960 --> 00:35:29.139 Yeah. 670 00:35:29.420 --> 00:35:32.900 And speaking of languages, how does JavaScript hit you for 671 00:35:32.920 --> 00:35:33.719 a math language? 672 00:35:35.599 --> 00:35:38.500 JavaScript is kind of, it's not. 673 00:35:38.519 --> 00:35:39.039 You can say it. 674 00:35:39.340 --> 00:35:39.840 It's okay. 675 00:35:40.760 --> 00:35:43.059 It's not the best language for computing. 676 00:35:43.099 --> 00:35:43.739 Yeah, right. 677 00:35:43.840 --> 00:35:46.280 The nice thing about it is that you have numbers 678 00:35:46.360 --> 00:35:49.360 and they're all the same. But that's when you do 679 00:35:49.429 --> 00:35:51.960 numerical stuff, that's also the, The problem. 680 00:35:52.219 --> 00:35:52.900 Right. Yeah. 681 00:35:53.179 --> 00:35:53.980 As we found out. 682 00:35:54.619 --> 00:35:57.300 We've talked a little bit about complex numbers so far 683 00:35:57.719 --> 00:36:01.480 in the library here. I don't know that I exactly 684 00:36:01.559 --> 00:36:05.139 understand everything when we talk about space of complex numbers. Because, 685 00:36:05.760 --> 00:36:07.699 I mean, I've always thought that not a number, you know, 686 00:36:07.719 --> 00:36:11.530 speaking of JavaScript, was such a computer thing. But is 687 00:36:11.570 --> 00:36:14.449 that something relevant in complex numbers as well? 688 00:36:14.750 --> 00:36:18.150 It's relevant in all of numerical computing. 689 00:36:18.679 --> 00:36:19.059 Oh, okay. 690 00:36:19.119 --> 00:36:21.539 So a complex number just has a real part and 691 00:36:21.559 --> 00:36:22.579 an imaginary part. 692 00:36:22.800 --> 00:36:23.019 Right. 693 00:36:23.409 --> 00:36:26.469 And once you work with those two, it's just real 694 00:36:26.510 --> 00:36:30.530 math again. There's nothing complex about it. So the same 695 00:36:31.090 --> 00:36:34.730 issues that you encounter in real numbers, you will encounter 696 00:36:34.750 --> 00:36:36.199 in complex numbers again. Right. 697 00:36:36.659 --> 00:36:40.119 And so problems like infinity and not a number, these 698 00:36:40.159 --> 00:36:41.619 are just things you have to contend with. 699 00:36:41.920 --> 00:36:42.119 Yeah. 700 00:36:42.519 --> 00:36:45.820 And that's one of the weird things. Not a number 701 00:36:46.099 --> 00:36:53.889 is a special thing. encoding in the binary floating point format. 702 00:36:54.579 --> 00:36:59.079 And they compare false. So any operation, any logical operation 703 00:36:59.739 --> 00:37:02.380 with not a number returns false, including itself. 704 00:37:03.960 --> 00:37:06.099 So not a number is also not a number. 705 00:37:06.320 --> 00:37:10.449 Well, yeah. So you have to special case all kinds 706 00:37:10.489 --> 00:37:15.510 of code to work with that to trap it. One 707 00:37:15.530 --> 00:37:18.900 of the Places where you can get not a number 708 00:37:19.219 --> 00:37:22.820 is if you try to compute the square root of 709 00:37:22.860 --> 00:37:23.559 a negative number. 710 00:37:23.880 --> 00:37:24.099 Right. 711 00:37:24.320 --> 00:37:25.800 Does that make an imaginary number? 712 00:37:26.119 --> 00:37:29.420 That would make an imaginary number, but it's outside of 713 00:37:29.519 --> 00:37:31.400 the number format. Right. 714 00:37:31.980 --> 00:37:34.780 I'm starting to feel like in this context, not a 715 00:37:34.800 --> 00:37:39.539 number is problematically like nulls are problematic, where you have 716 00:37:39.579 --> 00:37:42.619 to test for them, and they're hard to test against themselves. 717 00:37:43.460 --> 00:37:45.300 So they just have to build a set of exception 718 00:37:45.320 --> 00:37:45.980 cases around it. 719 00:37:47.159 --> 00:37:51.739 That's true, and it's more of an annoyance than anything. 720 00:37:52.320 --> 00:37:54.599 If you're careful, you won't encounter them. 721 00:37:54.940 --> 00:37:55.159 Right. 722 00:37:55.860 --> 00:38:02.780 But the other challenge is of maintaining precision. If you 723 00:38:02.800 --> 00:38:05.300 can do that, you're good. If you can't, then you 724 00:38:05.320 --> 00:38:08.849 can get things like dividing zero by zero, which is 725 00:38:08.909 --> 00:38:10.230 also not a number. 726 00:38:10.369 --> 00:38:10.949 Not a number. 727 00:38:10.969 --> 00:38:11.570 Yeah. 728 00:38:12.920 --> 00:38:15.360 That's fair. So, I mean, on one hand, I'm losing 729 00:38:15.389 --> 00:38:18.889 this library because I have a particular use case where 730 00:38:18.949 --> 00:38:22.570 I have a particular requirement for precision that perhaps doesn't 731 00:38:22.610 --> 00:38:24.519 fall into what's built into. 732 00:38:24.670 --> 00:38:24.889 NET. 733 00:38:24.969 --> 00:38:26.719 Does that make sense? Is that a reason to go 734 00:38:26.780 --> 00:38:28.079 into using the library? 735 00:38:29.380 --> 00:38:31.440 That's one possibility. We have. 736 00:38:32.800 --> 00:38:37.800 Big floats that can Do enormous ranges of numbers to 737 00:38:37.920 --> 00:38:39.550 whatever precision you want, basically. 738 00:38:39.610 --> 00:38:42.889 How big is a big float there, Jeff? A Google? 739 00:38:44.750 --> 00:38:47.769 I think the exponent is about 10 billion. 740 00:38:48.449 --> 00:38:48.570 Oh. 741 00:38:49.309 --> 00:38:51.909 And you can have like up to a couple of 742 00:38:51.929 --> 00:38:53.349 billion digits, something like that. 743 00:38:53.369 --> 00:38:54.929 So you could calculate with Googles. 744 00:38:55.590 --> 00:38:55.829 Yeah. 745 00:38:56.130 --> 00:38:56.409 Wow. 746 00:38:56.710 --> 00:39:00.389 A Google actually fits in a normal double floating boy number. 747 00:39:00.530 --> 00:39:00.869 Really? 748 00:39:01.070 --> 00:39:01.269 Wow. 749 00:39:01.329 --> 00:39:03.190 If it's 10 to the power 100. Right. 750 00:39:04.239 --> 00:39:09.679 It's not exact. Because we don't have enough bits

for that. But, yeah, 751 00:39:09.760 --> 00:39:10.920 it is within the range. 752 00:39:11.500 --> 00:39:14.619 Nice. Okay. But then now when I think about, you know, 753 00:39:14.679 --> 00:39:18.750 why would I want a library like this, I immediately 754 00:39:18.769 --> 00:39:22.869 head towards calculus. Because that's hard to do without a library. 755 00:39:22.989 --> 00:39:23.369 That's right. 756 00:39:23.849 --> 00:39:29.130 Well, more generally, the reason you would go to a 757 00:39:29.190 --> 00:39:35.639 library like this, is that avoiding the loss of precision 758 00:39:36.800 --> 00:39:42.739 is a challenge. Right? So we talked about every operation 759 00:39:42.800 --> 00:39:47.900 introduces potentially another additional small error. Right. There's also something 760 00:39:47.920 --> 00:39:52.900 called catastrophic cancellations. which is you have two numbers that 761 00:39:53.000 --> 00:39:59.300 almost have the same magnitude, and you subtract them. So 762 00:39:59.539 --> 00:40:02.059 the result is very small relative to those two numbers. 763 00:40:02.280 --> 00:40:02.780 Oh, okay. 764 00:40:02.840 --> 00:40:04.889 Well, your precision will plummet. 765 00:40:05.050 --> 00:40:07.210 Yeah, and turn it to a zero when it shouldn't be. 766 00:40:07.429 --> 00:40:07.670 Yeah. 767 00:40:08.150 --> 00:40:08.889 Right, okay. 768 00:40:09.150 --> 00:40:15.030 And then you get into other things like... One of 769 00:40:15.090 --> 00:40:18.420 the biggest challenges for me that I have to be 770 00:40:18.460 --> 00:40:23.130 always aware of is... Computer math is not quite like 771 00:40:23.449 --> 00:40:28.489 regular math. So, for example, the order of operations matters. 772 00:40:30.320 --> 00:40:32.659 In normal math, when you add three numbers, it doesn't 773 00:40:32.679 --> 00:40:34.119 really matter which order you do it in. 774 00:40:34.340 --> 00:40:34.519 No. 775 00:40:34.679 --> 00:40:39.300 But say you have 1 plus 10 to the minus 776 00:40:39.300 --> 00:40:41.079 20 plus minus 1. 777 00:40:41.079 --> 00:40:42.719 Oh, I see the problem already. 778 00:40:42.860 --> 00:40:46.639 So, 1 plus 10 to the minus 20, you don't 779 00:40:46.679 --> 00:40:50.329 have the precision to register that little thing you're adding, 780 00:40:50.750 --> 00:40:53.590 so that remains one. And then if you subtract again, 781 00:40:53.690 --> 00:40:57.000 it's zero. Whereas if you do one minus one and 782 00:40:57.039 --> 00:41:01.059 then add, it's zero plus your small number and you 783 00:41:01.119 --> 00:41:02.400 have a different result. 784 00:41:02.760 --> 00:41:06.940 Because the first item in the list is what defines 785 00:41:07.000 --> 00:41:09.050 the type that it's cast to, right? 786 00:41:09.070 --> 00:41:09.429 That's right. 787 00:41:09.550 --> 00:41:12.889 So the programming language defines the order and you have 788 00:41:12.909 --> 00:41:14.710 to make sure that you do things in the right order. 789 00:41:15.250 --> 00:41:19.050 And that can sneak up on you like A simple expression, 790 00:41:19.070 --> 00:41:22.849 a plus k minus 1, where a is a real number, 791 00:41:22.889 --> 00:41:25.090 k is an integer. That looks innocent, right? 792 00:41:25.670 --> 00:41:25.929 Yeah. 793 00:41:25.989 --> 00:41:29.750 Can't really go wrong with that. Well, what happens if 794 00:41:30.349 --> 00:41:34.139 a is a small number and k equals 1? Then 795 00:41:34.179 --> 00:41:36.860 you're going to have a plus 1. You're going to 796 00:41:36.920 --> 00:41:41.420 lose tons of precision there. And then subtract 1 again. 797 00:41:41.780 --> 00:41:45.599 So you've just lost lots of precision in that simple, 798 00:41:45.739 --> 00:41:47.019 innocent-looking operation. 799 00:41:47.630 --> 00:41:50.730 Yeah, you ended up at zero and it shouldn't have been. 800 00:41:50.889 --> 00:41:51.289 Yeah, or. 801 00:41:53.610 --> 00:41:57.449 Something close, but much less accurate than what you started 802 00:41:57.530 --> 00:41:57.829 out with. 803 00:41:58.110 --> 00:41:58.369 Right. 804 00:41:58.570 --> 00:42:03.369 Is there such a thing as a specialized computer and 805 00:42:03.449 --> 00:42:09.550 language that brings computer math closer to real math? 806 00:42:09.889 --> 00:42:14.159 You could say that there are symbolic computer systems, but 807 00:42:14.179 --> 00:42:15.340 that's really kind of cheating. 808 00:42:15.360 --> 00:42:15.739 Uh-huh. 809 00:42:16.360 --> 00:42:19.440 So I wouldn't say for practical use, not really. 810 00:42:19.460 --> 00:42:22.179 Okay. I mean, wasn't that what Fortran was about, was 811 00:42:22.219 --> 00:42:24.460 trying to get rid of these precision problems back in 812 00:42:24.480 --> 00:42:24.800 the day? 813 00:42:25.860 --> 00:42:30.969 Fortran was to make it easy to write out equations. 814 00:42:31.659 --> 00:42:34.630 It's literally derived from formula translation. 815 00:42:34.929 --> 00:42:35.150 Right. 816 00:42:35.789 --> 00:42:42.550 So eliminating the floating point traps and so on is 817 00:42:42.650 --> 00:42:45.090 really not practical to. 818 00:42:45.030 --> 00:42:48.989 Do in a In a language, you have to sort 819 00:42:49.010 --> 00:42:50.889 of choose your algorithm. 820 00:42:51.690 --> 00:42:51.929 Right. 821 00:42:52.710 --> 00:42:57.230 And so you have to, sometimes you get a formula 822 00:42:57.389 --> 00:43:00.880 and there's something that can blow up or where you 823 00:43:00.889 --> 00:43:03.780 can lose precision. And then you have to find a 824 00:43:04.940 --> 00:43:11.380 different path of obtaining the same result that doesn't have 825 00:43:11.420 --> 00:43:14.559 that problem. And that's the biggest challenge. 826 00:43:14.599 --> 00:43:17.039 Yeah, and so you're no longer just working on the 827 00:43:17.079 --> 00:43:19.340 math problem. You're working in the constraints of the computer. 828 00:43:19.420 --> 00:43:19.780 That's right. 829 00:43:19.940 --> 00:43:21.780 You have to adapt your math

problem to what the 830 00:43:21.800 --> 00:43:22.760 computer can do for you. 831 00:43:22.800 --> 00:43:27.199 That's right. And that's why it's hard. That's why so 832 00:43:29.239 --> 00:43:31.199 much time is spent on getting it right. 833 00:43:32.480 --> 00:43:34.940 And the problem is if you're not aware of the problems, 834 00:43:34.960 --> 00:43:37.719 you just write an expression. And in certain test cases, 835 00:43:37.760 --> 00:43:40.949 it works fine. And in other cases, it ruins everything. 836 00:43:41.090 --> 00:43:47.079 Yeah, and... Most cases you'll test are like mid-range, normal, 837 00:43:47.760 --> 00:43:52.650 everyday things. And sure, it'll work fine with that. Like, yeah, 838 00:43:52.670 --> 00:43:55.050 you might lose a digit or two, but nothing relevant. 839 00:43:55.530 --> 00:43:59.610 But then extreme cases happen, and then, yeah, you might 840 00:43:59.630 --> 00:44:00.329 run into trouble. 841 00:44:00.550 --> 00:44:03.550 Disasters. Should we go down some of the paths of these? 842 00:44:04.130 --> 00:44:06.110 different math sets you've done here, I'm just trying to 843 00:44:06.130 --> 00:44:11.469 figure out what a Gauss Cronrod numerical integrator is. You're 844 00:44:11.510 --> 00:44:15.309 making that up, Richard. I wish I was. I'm just 845 00:44:15.409 --> 00:44:19.110 reading through the spec here and going, oh boy. If 846 00:44:19.130 --> 00:44:21.760 you don't know what that is, you probably don't need one. 847 00:44:22.449 --> 00:44:29.300 Yeah, Gauss is the famous mathematician who pioneered numerical integration, 848 00:44:29.320 --> 00:44:31.420 so computing the area under a curve. 849 00:44:32.090 --> 00:44:33.789 Using approximations. 850 00:44:34.090 --> 00:44:35.110 You said Gauss, right? 851 00:44:35.429 --> 00:44:36.570 And Gauss, yeah. 852 00:44:36.849 --> 00:44:39.610 Is that what the Gaussian blur is based on? 853 00:44:39.849 --> 00:44:40.610 That's also him. 854 00:44:40.789 --> 00:44:48.340 Wow. Like anything Gauss, like the Gaussian distribution, Gaussian blur, 855 00:44:48.360 --> 00:44:50.280 all those things are all the same person. 856 00:44:50.619 --> 00:44:52.940 Wow. Right. Clever guy. 857 00:44:53.079 --> 00:44:53.320 Yeah. 858 00:44:53.539 --> 00:44:58.119 So one way to compute errors is you compute the 859 00:44:58.159 --> 00:45:00.610 same result in two different ways, one more accurate than. 860 00:45:00.489 --> 00:45:00.960 The other one. 861 00:45:01.460 --> 00:45:02.599 And then you compare results. 862 00:45:03.039 --> 00:45:03.260 Right. 863 00:45:03.760 --> 00:45:08.300 And Gauss-Krohn wrote is a way of doing that with 864 00:45:08.400 --> 00:45:13.150 reusing some of the calculations you've done so that you've, 865 00:45:14.550 --> 00:45:17.949 so to minimize extra work. So that's what that is. 866 00:45:18.289 --> 00:45:21.349 No, and I appreciate that. So now I'm thinking the 867 00:45:21.369 --> 00:45:24.489 software engineer in me is like, okay. We measure this 868 00:45:24.570 --> 00:45:26.849 particular problem space in two different ways and then use 869 00:45:26.869 --> 00:45:28.809 an integrator to get what we think is the most 870 00:45:28.909 --> 00:45:29.989 accurate possible answer. 871 00:45:30.150 --> 00:45:30.510 That's right. 872 00:45:30.670 --> 00:45:32.889 Yeah, smart. And it's good to have a tool. You 873 00:45:32.909 --> 00:45:34.880 could try and code your way around that. You'd probably 874 00:45:34.889 --> 00:45:36.219 screw it up. Use the tool. 875 00:45:36.340 --> 00:45:36.739 That's right. 876 00:45:36.989 --> 00:45:41.239 And so that particular one is used for what's called 877 00:45:41.260 --> 00:45:47.360 adaptive integration, which means if you have a curve that's 878 00:45:47.440 --> 00:45:51.739 really oscillating a lot, like changes very quickly, if you 879 00:45:51.989 --> 00:45:54.750 try to approximate it with a few points, you're going 880 00:45:54.769 --> 00:45:59.250 to be way off. And so by computing the error, 881 00:45:59.289 --> 00:46:03.369 you can say, okay, we're good in this part of 882 00:46:03.389 --> 00:46:06.590 the function, but here we need to dig deeper and 883 00:46:06.639 --> 00:46:11.360 be more precise. So you do a recalculation there. What's 884 00:46:11.420 --> 00:46:14.780 the error now? And you keep doing that until your 885 00:46:14.800 --> 00:46:16.239 result is accurate enough. 886 00:46:16.900 --> 00:46:17.880 Accurate enough. 887 00:46:18.840 --> 00:46:23.860 I imagine FFTs, Fast Fourier transforms. I only know a 888 00:46:23.889 --> 00:46:26.280 lot of this stuff because, you know, the Gaussian blur 889 00:46:26.320 --> 00:46:28.579 you use in Photoshop and other things like that. And 890 00:46:28.659 --> 00:46:33.639 the FFTs we use in noise reduction algorithms in Adobe Audition. 891 00:46:34.199 --> 00:46:37.380 And I've been using them ever since I've been recording 892 00:46:37.420 --> 00:46:44.440 with digital audio. But from what I understand about noise reduction, 893 00:46:44.480 --> 00:46:48.880 it uses a fast Fourier transform and you select the 894 00:46:48.920 --> 00:46:52.019 number of points. And what it does in the audio 895 00:46:52.059 --> 00:46:56.409 world is it acts as, let's say it's 8,000 points. 896 00:46:57.050 --> 00:47:04.750 It's an 8,000 band compressor, right? So you have a 897 00:47:04.769 --> 00:47:09.010 compressor with three bands, high, low, and mid, or high, mid, 898 00:47:09.070 --> 00:47:12.730 and low, whatever. But if you break that up into 899 00:47:13.150 --> 00:47:18.650 the frequency spectrum into 8,000 bands, then it can compress 900 00:47:19.170 --> 00:47:23.829 each band. band individually using a fast Fourier transform I 901 00:47:23.869 --> 00:47:26.230 don't know how but I know it works. 902 00:47:27.590 --> 00:47:35.500 Fourier transform basically turns a signal into its frequencies and 903 00:47:35.539 --> 00:47:37.940 so then you can filter out high frequencies or mid 904

00:47:38.000 --> 00:47:44.199 or low or like apply equalizers and then transform back 905 00:47:45.019 --> 00:47:48.119 to get your new signal with the high frequencies filtered 906 00:47:48.219 --> 00:47:48.769 out Right. 907 00:47:48.829 --> 00:47:51.269 Makes a lot of sense, especially we use an 8K 908 00:47:51.789 --> 00:47:55.210 FFT size for noise reduction. Always have. And it seemed 909 00:47:55.230 --> 00:47:58.559 to be the sweet spot for audio, for speaking anyway. 910 00:47:59.440 --> 00:48:00.519 Just one of those things. 911 00:48:00.920 --> 00:48:01.119 Yeah. 912 00:48:01.360 --> 00:48:04.579 Wow. Should we, some other areas to explore here, Jeff? 913 00:48:04.619 --> 00:48:05.949 What do you want to, what would you like to 914 00:48:05.989 --> 00:48:09.429 talk about? Maybe some Jebyshev polynomials? 915 00:48:09.869 --> 00:48:12.349 Jebyshev is one of the luckiest people in the world. 916 00:48:14.230 --> 00:48:16.219 This is a mathematician, I presume. 917 00:48:16.360 --> 00:48:21.960 He's a mathematician. I'm not even sure which century he's from. 918 00:48:22.260 --> 00:48:22.500 Right. 919 00:48:22.880 --> 00:48:27.719 But he played with a certain type of polynomials that 920 00:48:28.929 --> 00:48:32.329 looked interesting. And so they ended up being named after him. 921 00:48:33.449 --> 00:48:37.429 And these days they're used all over the place. Right. 922 00:48:38.349 --> 00:48:43.559 Because they're defining property. What makes them useful is that 923 00:48:44.539 --> 00:48:49.539 They're very even. They oscillate, yes, but they oscillate within 924 00:48:49.559 --> 00:48:55.039 a narrow band, and it's the narrowest possible band. Oh, interesting. 925 00:48:55.340 --> 00:49:02.170 JPL uses that for their planetary models. They will give 926 00:49:02.269 --> 00:49:08.789 out positions of planets and asteroids and everything as a 927 00:49:08.949 --> 00:49:18.429 series of Cheverchev polynomials. because you can very accurately model 928 00:49:19.289 --> 00:49:23.650 basically any curve using them. And what I was saying 929 00:49:23.710 --> 00:49:32.510 about controlling the growth of your errors, they're extremely favorable 930 00:49:32.550 --> 00:49:36.789 that way. So you will get minimal error propagation, which is, again, why. 931 00:49:36.650 --> 00:49:39.650 They're so common. I looked him up. He was a 932 00:49:39.710 --> 00:49:40.340 Russian from the 1800s. 933 00:49:40.389 --> 00:49:40.610 Yeah. 934 00:49:40.630 --> 00:49:45.670 Sounds right. That's a lot of mathematicians, actually, I think. 935 00:49:45.889 --> 00:49:48.630 And he was at a time of defining all this stuff. So, again, 936 00:49:49.230 --> 00:49:51.510 you've come back to this a few times, Jeff. It's 937 00:49:51.550 --> 00:49:55.449 like you're trying to work through a set of data 938 00:49:55.469 --> 00:49:58.360 and get an aggregate or some kind of valuation from 939 00:49:58.400 --> 00:49:59.880 it without introducing a lot of error. 940 00:50:00.059 --> 00:50:00.260 Yeah. 941 00:50:00.320 --> 00:50:02.159 And these are the kinds of tools you use to 942 00:50:02.179 --> 00:50:02.940 try and keep the errors. 943 00:50:03.019 --> 00:50:06.900 And the problem is, too– As I said earlier, as 944 00:50:06.940 --> 00:50:10.420 soon as you bring a real world number into your 945 00:50:10.460 --> 00:50:14.510 computing system, you have some deviation from reality. And there's 946 00:50:14.550 --> 00:50:15.489 another famous. 947 00:50:15.650 --> 00:50:17.889 Because the computer does an approximation on it. 948 00:50:17.969 --> 00:50:18.550 Yeah. 949 00:50:19.329 --> 00:50:24.010 There's another famous and rather tragic example from the Gulf 950 00:50:24.030 --> 00:50:28.610 War in 1991. There was a Scud missile heading towards 951 00:50:28.630 --> 00:50:34.070 a U.S. base in Tehran in Saudi Arabia. And they 952 00:50:34.090 --> 00:50:38.550 had a Patriot system. for air defense, but it failed, 953 00:50:38.630 --> 00:50:44.539 it missed. And the reason it missed was round off error. 954 00:50:45.400 --> 00:50:50.260 They were counting time by incrementing a counter every tenth 955 00:50:50.280 --> 00:50:53.980 of a second. So after about four days, the counter 956 00:50:54.019 --> 00:50:57.630 was at something like three and a half million. And 957 00:50:57.670 --> 00:51:03.849 then they computed the current time by multiplying that counter 958 00:51:03.869 --> 00:51:09.989 by by 0.1. 0.1 is not a floating point number, 959 00:51:10.090 --> 00:51:12.929 not a binary floating point number. So there's this very 960 00:51:13.010 --> 00:51:18.829 tiny error there of about 95 nanoseconds. But when you 961 00:51:18.869 --> 00:51:24.010 multiply 9 to 5 nanoseconds by 3.5 million, you get 962 00:51:24.050 --> 00:51:28.360 about three-tenths of a second. And missiles fly very fast 963 00:51:28.380 --> 00:51:31.119 and cover a lot of ground in that time. And 964 00:51:31.179 --> 00:51:35.949 so the interceptor missed And unfortunately, I think 28 people 965 00:51:35.969 --> 00:51:41.400 died in that attack. So, it can have very serious consequences. 966 00:51:41.940 --> 00:51:42.599 Yeah, no kidding. 967 00:51:42.880 --> 00:51:45.960 We were talking about in the news stories, Boeing and 968 00:51:45.980 --> 00:51:50.300 the problems that they had. And I wonder if, I mean, 969 00:51:50.320 --> 00:51:56.969 it was obvious incompetence in a culture of, you know, 970 00:51:57.090 --> 00:52:00.170 not reporting the truth and trying to appease the higher-ups 971 00:52:00.230 --> 00:52:03.780 and all that stuff and sycophancy, but I wonder if 972 00:52:04.119 --> 00:52:10.539 any of that stemmed from having bad algorithms or bad math. 973 00:52:11.440 --> 00:52:11.800 Do you know? 974 00:52:12.840 --> 00:52:20.920 I have no idea. There have been mistakes with the 975 00:52:20.960 --> 00:52:24.699 Ariane rocket and the example you gave too earlier. 976 00:52:24.780 --> 00:52:26.920 Sure, which I think is

a really interesting one just 977 00:52:26.940 --> 00:52:30.010 because they– changed the precision on the number and then 978 00:52:30.369 --> 00:52:32.650 introduced it into a different rocket that behaved differently and 979 00:52:32.829 --> 00:52:35.909 that number suddenly was a huge problem. And more importantly, 980 00:52:35.929 --> 00:52:39.409 the software doesn't get an overflow and the software just 981 00:52:39.449 --> 00:52:42.269 treats it as a number still, not acknowledging that, no, 982 00:52:42.289 --> 00:52:44.920 that's not a valid number and you should stop what 983 00:52:44.940 --> 00:52:46.539 you're doing. Whatever you do from here is going to 984 00:52:46.579 --> 00:52:52.179 be worse, not better. The MCAS story, which was part 985 00:52:52.199 --> 00:52:54.760 of that 737 MAX problem, is a complicated one and 986 00:52:54.800 --> 00:52:59.079 probably none Appropriate here, but yeah, it was the decision 987 00:52:59.159 --> 00:53:03.039 on hardware and software and how you communicated to the 988 00:53:03.099 --> 00:53:07.429 pilots combined that creates that situation. 989 00:53:07.849 --> 00:53:13.710 Speaking of radiation doses, there's also a story about a 990 00:53:13.789 --> 00:53:20.880 system to administer the radiation where some people got bad 991 00:53:20.920 --> 00:53:26.019 burns and it turned out They looked into it, maybe 992 00:53:26.079 --> 00:53:28.619 as the operator not experienced. And no, the operator is 993 00:53:28.659 --> 00:53:32.179 very experienced. And actually that turned out to be the 994 00:53:32.219 --> 00:53:36.940 problem because they entered the information so quickly that the 995 00:53:36.980 --> 00:53:42.360 system couldn't keep up and skipped an input. And that 996 00:53:42.420 --> 00:53:50.699 led to overdoses. So there's all kinds of like the 997 00:53:50.739 --> 00:53:53.800 numerical part is one thing, but there's also the good 998 00:53:54.000 --> 00:54:01.789 software practices of making allowances for exceptions and treating exceptional 999 00:54:01.829 --> 00:54:05.010 conditions adequately and correctly. 1000 00:54:05.269 --> 00:54:10.949 Yeah. Yeah. It's interesting to try and write software that 1001 00:54:11.010 --> 00:54:13.079 contends with that kind of thing because the consequence was 1002 00:54:13.119 --> 00:54:17.500 so serious. You know, they're just sort of recognizing that 1003 00:54:17.559 --> 00:54:23.449 the data doesn't make sense. What's reasonable. before it actually runs. 1004 00:54:24.369 --> 00:54:30.030 The Therac-25 issue, that was the radiation treatment where if 1005 00:54:30.050 --> 00:54:33.630 you entered the data too quickly, software went into a 1006 00:54:33.650 --> 00:54:34.309 race condition. 1007 00:54:35.250 --> 00:54:38.650 And one thing they did, I believe, in that instance 1008 00:54:38.789 --> 00:54:46.179 is the previous version of that equipment had hardware guards. Right. 1009 00:54:46.380 --> 00:54:50.239 So if the radiation was too high or voltage or 1010 00:54:50.320 --> 00:54:54.949 whichever way they measured it, it would refuse to do that. 1011 00:54:55.449 --> 00:54:57.510 But they took those off and they replaced them with 1012 00:54:57.550 --> 00:55:01.150 software tests. That obviously didn't work. 1013 00:55:01.550 --> 00:55:03.929 Yeah, obviously created other consequences, no question. 1014 00:55:04.329 --> 00:55:08.449 So your point is well taken. Math is kind of important. 1015 00:55:08.489 --> 00:55:14.780 To get right. Well, yeah, precision. I don't know that 1016 00:55:14.820 --> 00:55:18.920 we even now actually understand fully the compromises that were 1017 00:55:18.960 --> 00:55:21.019 made to store numbers in computers efficiently. 1018 00:55:22.679 --> 00:55:26.599 They did a pretty good job, actually, with the standard 1019 00:55:28.579 --> 00:55:37.769 IEEE 754 format. In some ways, it's quite ingenious. The numerical, 1020 00:55:37.929 --> 00:55:40.829 if you compare the bit value, if you look at 1021 00:55:40.869 --> 00:55:46.340 it as a 64-bit integer, it is in the correct 1022 00:55:46.380 --> 00:55:50.820 sort order. So you can compare the numbers as integers 1023 00:55:50.840 --> 00:55:54.710 and and have the correct sort order, except for. 1024 00:55:54.630 --> 00:56:00.090 The not a number cases, which are an annoyance. 1025 00:56:01.250 --> 00:56:06.260 And there's another problem that's not obvious at first sight. 1026 00:56:07.940 --> 00:56:10.760 Because of the format, you always have an integer times 1027 00:56:10.800 --> 00:56:14.219 a power of two. And so there are as many 1028 00:56:14.619 --> 00:56:18.469 floating point numbers between one and two as there are 1029 00:56:18.530 --> 00:56:23.380 between two and four, or four and eight. in 16, 1030 00:56:23.380 --> 00:56:29.099 so they've become scarcer and sparser, the more, the larger 1031 00:56:29.119 --> 00:56:31.840 your numbers get, and they get closer and closer together. 1032 00:56:31.860 --> 00:56:34.780 The smaller your numbers get. 1033 00:56:36.280 --> 00:56:38.400 And then the question is, well, what do you do 1034 00:56:38.440 --> 00:56:43.570 close to zero? And the solution they found was, well, 1035 00:56:44.489 --> 00:56:48.829 let's just switch from a floating point format into two 1036 00:56:49.309 --> 00:56:52.500 times a power of two. to a fixed point format. 1037 00:56:53.860 --> 00:57:01.349 And so all the numbers with exponent zero are called 1038 00:57:01.630 --> 00:57:07.050 subnormal numbers and they are a fixed point format. So 1039 00:57:07.070 --> 00:57:11.610 they are that number interpreted as an integer times, I 1040 00:57:11.630 --> 00:57:12.329 think it's two to. 1041 00:57:12.250 --> 00:57:13.250 The power minus 1,075. 1042 00:57:13.250 --> 00:57:19.590 So that when you get to zero, You have what 1043 00:57:19.610 --> 00:57:22.980 they call gradual underflow. You don't just cut to zero 1044 00:57:23.000 --> 00:57:27.579 straight away. You have

like a little bit of breathing 1045 00:57:27.619 --> 00:57:29.000 room to get there. 1046 00:57:29.820 --> 00:57:31.900 Yeah, this is way more complicated than you think about. 1047 00:57:31.920 --> 00:57:33.409 Most of the time we just use numbers and don't 1048 00:57:33.429 --> 00:57:35.949 worry about it. Sometimes you want integers and sometimes you 1049 00:57:35.969 --> 00:57:40.829 want floating point and you're fine. But then this is here. 1050 00:57:41.010 --> 00:57:43.550 I've just looked at this huge roster of capabilities that 1051 00:57:43.590 --> 00:57:47.019 are in all these exception cases. All right. How do 1052 00:57:47.039 --> 00:57:49.039 people figure out they need your tool, Jeff? 1053 00:57:49.280 --> 00:57:56.050 Well, most people just need some kind of calculation where 1054 00:57:56.090 --> 00:58:01.710 they need the level of extraction that our library provides. 1055 00:58:02.250 --> 00:58:06.630 So if you have to solve a set of equations, okay, 1056 00:58:06.650 --> 00:58:10.230 you can do it all yourself and try to figure 1057 00:58:10.250 --> 00:58:11.909 out how to do it efficiently. 1058 00:58:11.929 --> 00:58:12.389 Mm-hmm. 1059 00:58:12.869 --> 00:58:15.150 Or you can use my library and just say, okay, 1060 00:58:15.170 --> 00:58:16.860 these are a number of delegates. 1061 00:58:17.199 --> 00:58:19.300 And to be clear, your library is not free. 1062 00:58:19.619 --> 00:58:20.059 No, it's not. 1063 00:58:20.360 --> 00:58:22.860 Yeah. And not that I have a problem with that. 1064 00:58:22.880 --> 00:58:24.460 It makes sense. It sounds like you've done a ton 1065 00:58:24.500 --> 00:58:28.380 of work. And it's worth it for the folks. If 1066 00:58:28.420 --> 00:58:30.070 you need it, you need it. And you should pay 1067 00:58:30.090 --> 00:58:30.239 for it. 1068 00:58:30.250 --> 00:58:31.769 If you need it, you need it. That's right. 1069 00:58:31.789 --> 00:58:32.150 That's right. 1070 00:58:33.349 --> 00:58:35.369 This is literally a tool to save lives and stop 1071 00:58:35.389 --> 00:58:36.809 spacecraft from exploding. Yeah. 1072 00:58:37.969 --> 00:58:42.130 Yeah. talk about performance a little bit. Uh, some of the, 1073 00:58:42.269 --> 00:58:45.349 I mean, the.net framework has gotten more and more performant 1074 00:58:45.369 --> 00:58:48.880 with every release. Was there ever a time when you considered, 1075 00:58:49.139 --> 00:58:51.699 you know, dropping to assembler to do stuff because it 1076 00:58:51.760 --> 00:58:52.800 wasn't fast enough? 1077 00:58:52.940 --> 00:58:56.440 Well, we've been doing this for 20 years and, um, 1078 00:58:58.199 --> 00:59:05.400 we've seen a few performance, uh, concepts come and go. 1079 00:59:05.400 --> 00:59:07.760 Uh, when, uh. 1080 00:59:07.769 --> 00:59:14.420 The uh, task parallel library was first introduced around 2010, 1081 00:59:14.420 --> 00:59:18.039 that seemed to be the thing to speed things up. Uh, 1082 00:59:18.260 --> 00:59:21.099 turned out there was so much overhead that it was 1083 00:59:21.239 --> 00:59:26.500 limited in what we could do with it. Um, so 1084 00:59:27.380 --> 00:59:31.530 one example of where I did, um, role my own, 1085 00:59:31.590 --> 00:59:38.130 so to speak, is big integer. The initial implementation that 1086 00:59:38.300 --> 00:59:46.260 shift with. NET 4.0 in 2010 was adequate for small sizes, 1087 00:59:46.300 --> 00:59:52.099 but as soon as your numbers got large, it got 1088 00:59:52.900 --> 00:59:58.440 slower and slower. And so we did some work there 1089 00:59:58.480 --> 01:00:03.230 to make a faster version of that, But I really 1090 01:00:03.269 --> 01:00:04.150 have to give it to the. 1091 01:00:04.369 --> 01:00:05.010 NET guys. 1092 01:00:05.230 --> 01:00:08.550 In recent years, they've done so much to bring their 1093 01:00:08.590 --> 01:00:17.619 numerical side of things forward into what's actually now to 1094 01:00:17.659 --> 01:00:21.619 the point where we're considering giving up our big integer 1095 01:00:21.980 --> 01:00:22.860 and just using the. 1096 01:00:22.960 --> 01:00:24.079 NET standard version. 1097 01:00:25.500 --> 01:00:28.989 Do you utilize span of t? I know that's a 1098 01:00:29.050 --> 01:00:29.909 huge win. 1099 01:00:29.929 --> 01:00:31.309 We use it all the time. 1100 01:00:31.630 --> 01:00:31.849 Yeah. 1101 01:00:31.989 --> 01:00:32.329 Oh, wow. 1102 01:00:32.550 --> 01:00:36.150 All the time because, well, one of the advantages, too, 1103 01:00:36.349 --> 01:00:41.360 is a span can be over managed memory, but it 1104 01:00:41.380 --> 01:00:44.980 can also be over unmanaged memory, like anything you get 1105 01:00:45.039 --> 01:00:53.119 from a third-party library or application. And so using span 1106 01:00:53.239 --> 01:00:58.510 allows us to use the same code for– Managed memory, 1107 01:00:59.329 --> 01:01:02.670 so vectors stored in managed memory or in native memory. 1108 01:01:03.829 --> 01:01:07.230 And then the performance, too, it's very compact. It lets you, 1109 01:01:08.170 --> 01:01:11.469 and it's very much optimized more and more. It's actually 1110 01:01:11.489 --> 01:01:16.760 interesting when we look at our test suite. You can 1111 01:01:16.860 --> 01:01:18.690 see we still support. 1112 01:01:18.679 --> 01:01:20.059 NET 4.6.2 and. NET standards. 1113 01:01:25.139 --> 01:01:27.739 And you can see in our execution times of the 1114 01:01:27.780 --> 01:01:31.219 test suite how long it takes for each edition. 1115 01:01:32.570 --> 01:01:33.090 To run. 1116 01:01:34.250 --> 01:01:39.849 And without even changing any code, you can see a 1117 01:01:39.889 --> 01:01:45.300 progression by like every edition is like 10% faster overall. 1118 01:01:46.099 --> 01:01:47.719 And it's just a runtime that does that. 1119 01:01:47.940 --> 01:01:51.820 Yep. And overhead, memory overhead has also gone way down. 1120 01:01:52.039 --> 01:01:52.880 Yeah. 1121 01:01:53.119 --> 01:01:56.530 Just wonderful. Well, it's good to see that

you picked 1122 01:01:56.550 --> 01:01:57.190 the right horse. 1123 01:01:58.230 --> 01:01:59.489 Yeah, 20-plus year run. 1124 01:02:00.030 --> 01:02:01.170 Yeah. 1125 01:02:01.409 --> 01:02:04.989 I'm very impressed with the work they've been doing. And 1126 01:02:05.050 --> 01:02:12.469 also in the library itself, when, again, Complex Numbers first. 1127 01:02:12.269 --> 01:02:13.800 Came out, also in. 1128 01:02:13.429 --> 01:02:20.849 NET 4, it was really like you're– textbook or school 1129 01:02:20.869 --> 01:02:26.280 book implementation. It was just the formulas without really understanding 1130 01:02:26.340 --> 01:02:28.559 the intricacies of. 1131 01:02:30.099 --> 01:02:31.559 How to get precise results. 1132 01:02:32.699 --> 01:02:36.219 Even in there, when you computed the square root of 1133 01:02:36.260 --> 01:02:41.949 minus one, which should be purely imaginary I, because that's 1134 01:02:41.969 --> 01:02:46.550 the definition of the imaginary unit, it was off, it 1135 01:02:46.590 --> 01:02:52.150 wasn't correct. But in the last couple of years, and 1136 01:02:52.210 --> 01:02:56.650 now with. NET 11, they've done a ton of work 1137 01:02:56.730 --> 01:03:01.650 to clean that up. And we're not quite ready to 1138 01:03:01.710 --> 01:03:10.280 give up our complex number implementation, but we're seriously considering it. So, again, 1139 01:03:10.920 --> 01:03:12.500 great job,. NET team. 1140 01:03:12.679 --> 01:03:14.280 We should pass it along to Steve and Todd. Those 1141 01:03:14.320 --> 01:03:15.420 guys are freaking brilliant. 1142 01:03:15.619 --> 01:03:19.429 They are, yeah. Well, Jeffrey, thanks for hanging with us. 1143 01:03:19.929 --> 01:03:22.130 We went a little bit over, but that's only because 1144 01:03:22.190 --> 01:03:24.769 we had such a long intro. But it was great 1145 01:03:24.849 --> 01:03:29.219 just going through your interview without an interruption. And this 1146 01:03:29.320 --> 01:03:32.860 is awesome stuff. And I'm actually a little impressed with 1147 01:03:32.960 --> 01:03:34.840 both Richard and I for keeping up with you. 1148 01:03:35.980 --> 01:03:37.860 I think Jeff is a great explainer. 1149 01:03:37.920 --> 01:03:38.760 You are, yeah. 1150 01:03:38.800 --> 01:03:39.840 Which I really appreciate. 1151 01:03:40.679 --> 01:03:41.119 Thank you. 1152 01:03:41.460 --> 01:03:43.789 And good luck in the future. And thanks very much. 1153 01:03:43.849 --> 01:03:44.269 Thank you. 1154 01:03:44.309 --> 01:03:47.889 And we will talk to you dear listener next time on. 1155 01:03:47.599 --> 01:03:48.619 NET Rocks. 1156 01:04:10.340 --> 01:04:13.039 NET Rocks is brought to you by Franklin's Net and 1157 01:04:13.099 --> 01:04:17.800 produced by Plop Studios. a full-service audio, video, and post-production 1158 01:04:17.840 --> 01:04:21.849 facility located physically in New London, Connecticut, and, of course, 1159 01:04:21.909 --> 01:04:30.050 in the cloud, online at pwop.com. Visit our website at dotnetrocks.com 1160 01:04:30.489 --> 01:04:35.170 for RSS feeds, downloads, mobile apps, comments, and access to 1161 01:04:35.190 --> 01:04:38.590 the full archives going back to show number one, recorded 1162 01:04:38.630 --> 01:04:42.489 in September 2002. And make sure you check out our sponsors. 1163 01:04:42.769 --> 01:04:46.139 They keep us in business. Now go write some code. 1164 01:04:46.179 --> 01:04:46.820 See you next time.