1 00:00:00,000 --> 00:00:03,660 Okay, so I want to spend a little time on the term, "Big Data" and I'm not too 2 00:00:03,660 --> 00:00:08,778 concerned with any sort of technical definition of it, of the term. 3 00:00:08,778 --> 00:00:12,738 Because it probably doesn't exist but I want to arm you with some of the language 4 00:00:12,738 --> 00:00:16,395 that people use when they describe Big Data. 5 00:00:16,395 --> 00:00:24,005 So you know, you can speak intelligently about it when, when asked. 6 00:00:24,005 --> 00:00:26,319 Okay? So, the, probably the main thing to 7 00:00:26,319 --> 00:00:30,339 recognize is this notion of the three V's of Big Data which are volume, velocity, 8 00:00:30,339 --> 00:00:34,222 and variety. And we talked a little bit about this in 9 00:00:34,222 --> 00:00:37,845 a previous segment. So just to repeat, you know, volume is 10 00:00:37,845 --> 00:00:43,430 the size of the data. And you measure in bytes or number of 11 00:00:43,430 --> 00:00:48,596 rows or number of objects or what have you, sort of the vertical dimension of 12 00:00:48,596 --> 00:00:53,782 the data. What I'll say here is the latency of the 13 00:00:53,782 --> 00:00:57,747 data processing relative to the demand for interactivity, and that's maybe a 14 00:00:57,747 --> 00:01:01,030 mouthful. But, what I mean by that is you know, how 15 00:01:01,030 --> 00:01:04,250 fast is it coming based on how fast it needs to be consumed. 16 00:01:04,250 --> 00:01:08,475 And so, there's a lot of applications for which interactive response time are 17 00:01:08,475 --> 00:01:12,633 increasingly important, if not directly important. 18 00:01:12,633 --> 00:01:14,190 Okay? And so, when this becomes the bottle 19 00:01:14,190 --> 00:01:16,732 neck, when this becomes the challenge, then this will also start to become 20 00:01:16,732 --> 00:01:20,566 pretty relevant. And the one that I think is really pretty 21 00:01:20,566 --> 00:01:23,946 interesting to me and is near and dear to my heart and with my research is notion 22 00:01:23,946 --> 00:01:27,500 of variety. And so here the problem is, you know, an 23 00:01:27,500 --> 00:01:30,450 increasing number of different data sources are being applied for any 24 00:01:30,450 --> 00:01:33,785 particular task. So you need to pull out, you know, ASI 25 00:01:33,785 --> 00:01:36,785 files as well as download data from the web as well as pull data out of some 26 00:01:36,785 --> 00:01:41,218 database. As well as you use some of those sequel 27 00:01:41,218 --> 00:01:45,130 system, and so on. And the integration of all this data 28 00:01:45,130 --> 00:01:49,351 sources, is, a, pretty significant problem, and can end up occupying, a lot 29 00:01:49,351 --> 00:01:53,102 of your time. So I made this point, a couple of 30 00:01:53,102 --> 00:01:56,978 segments ago, about researches who spend near 90% of their time, quote, handling 31 00:01:56,978 --> 00:01:59,435 data. This is where a lot of that time is 32 00:01:59,435 --> 00:02:01,180 going. There's a notion of variety. 33 00:02:01,180 --> 00:02:03,930 Okay. So all three of these are relevant in 34 00:02:03,930 --> 00:02:08,313 performing sort of data science tasks. Alright, let me give you another notion 35 00:02:08,313 --> 00:02:10,970 and I'm going to go back to use science examples. 36 00:02:10,970 --> 00:02:14,170 And you've seen some of these before, but if you sort of make a plot of number of 37 00:02:14,170 --> 00:02:17,990 bytes on the Y-axis versus number of data sources. 38 00:02:17,990 --> 00:02:21,753 Maybe columns of data in single table or columns of data across multiple tables or 39 00:02:21,753 --> 00:02:25,260 a number of distinct data sources on the X axis. 40 00:02:25,260 --> 00:02:30,930 You can sort of, map out different fields of study or different problems and sort 41 00:02:30,930 --> 00:02:36,822 of, see where they lie. And so typically Astronomy has been the 42 00:02:36,822 --> 00:02:41,929 challenge by the sheer volume of data. So that's right about here we're high on 43 00:02:41,929 --> 00:02:44,724 the Y axis but you know, but the number of actual sources in astronomy is not too 44 00:02:44,724 --> 00:02:47,854 high. There's telescope there's these spectral 45 00:02:47,854 --> 00:02:51,039 imagers and then there's the simulation of the, of the, of the galaxy and so 46 00:02:51,039 --> 00:02:54,880 that's relatively few. In say the ocean sciences and certainly 47 00:02:54,880 --> 00:02:59,050 in life sciences although I only show you know, one example here. 48 00:02:59,050 --> 00:03:01,882 The variety is really more of a challenge, the actual shear scale is not 49 00:03:01,882 --> 00:03:04,954 as high as the, you know, hundreds of[UNKNOWN] bytes that could be generated 50 00:03:04,954 --> 00:03:09,870 by these, these telescopic projector like a large[UNKNOWN] telescope. 51 00:03:11,670 --> 00:03:15,489 but the number of different types of instruments you can, use to acquire data 52 00:03:15,489 --> 00:03:20,015 is large and ever-growing, right? So you have these glider systems that 53 00:03:20,015 --> 00:03:24,790 will go out for months at a time and kind of porpoise through the water. 54 00:03:24,790 --> 00:03:29,080 you have autonomous underwater vehicles that are more for short term missions. 55 00:03:29,080 --> 00:03:32,230 you know there, there's oceanographic cruises where they deploy these 56 00:03:32,230 --> 00:03:35,430 conductivity temperature and depth instrumensts that can take profiles of 57 00:03:35,430 --> 00:03:39,300 the water, right. So this is you know, at a fixed XY and a 58 00:03:39,300 --> 00:03:43,265 varying Z and a variying T at a varying depth at a varying time while the gliders 59 00:03:43,265 --> 00:03:48,189 are sort of varying in all four dimensions. 60 00:03:48,189 --> 00:03:50,483 You have these simulations that are probably one of the largest sources of 61 00:03:50,483 --> 00:03:53,214 information, right. So these can be[UNKNOWN] scales, sort of. 62 00:03:53,214 --> 00:03:57,758 At the order of the entire northern hemisphere, or whole eastern pacific, or 63 00:03:57,758 --> 00:04:01,828 there could be models, of a particular bay. 64 00:04:01,828 --> 00:04:06,443 Or inlet or estuary connected to a river or connected to the open ocean or a much 65 00:04:06,443 --> 00:04:11,049 smaller scale thing. So, there's a lot of diversity there. 66 00:04:12,060 --> 00:04:14,916 And I say stations to mean these sort of fixed stations where there's a particular 67 00:04:14,916 --> 00:04:18,655 sense that are deployed to one location and just measuring across time. 68 00:04:18,655 --> 00:04:22,809 ADCP is a Acoustic Doppler something profilor, where they're still using sound 69 00:04:22,809 --> 00:04:26,715 waves to record the time that the sound waves take to bounce off a particular 70 00:04:26,715 --> 00:04:32,220 matter in the ocean. And they can therefore measure velocity. 71 00:04:32,220 --> 00:04:35,040 And so this gives you an entire profile of the velocities in the ocean. 72 00:04:35,040 --> 00:04:37,640 And you can mount these on the sea floor pointing upwards, or you can mount them 73 00:04:37,640 --> 00:04:40,440 on the bottom of a boat pointing downwards, and so on. 74 00:04:40,440 --> 00:04:43,368 And then there's satellite images that measure sort of sea color and wave 75 00:04:43,368 --> 00:04:44,980 breaking as well. Okay. 76 00:04:44,980 --> 00:04:49,752 So fine. So just a little more on the term Big 77 00:04:49,752 --> 00:04:53,040 Data. a, a quote. 78 00:04:53,040 --> 00:04:55,900 The notion that Mike Franklin at the University of Berkeley uses, which I like 79 00:04:55,900 --> 00:04:58,628 is that you know, "Big Data is really relative rigtht, it's any data that's 80 00:04:58,628 --> 00:05:02,255 expensive to manage and hard to extract value from". 81 00:05:02,255 --> 00:05:05,153 So it's not so much about a particular cut off, you know, what makes it big, is 82 00:05:05,153 --> 00:05:08,235 it petabyte scale is big versus terabyte scale is small or gigabyte scale is very 83 00:05:08,235 --> 00:05:11,930 small since it fits in memory on your machine. 84 00:05:11,930 --> 00:05:13,814 You know, not necessarily. It depends on what you're trying to do 85 00:05:13,814 --> 00:05:16,024 with it and it depends on what sort of resources and infrastructure you have to 86 00:05:16,024 --> 00:05:20,098 bring to bear on the problem. And so in some sense, difficult data is 87 00:05:20,098 --> 00:05:24,356 perhaps what big data really means. It's not so much really big, it's about 88 00:05:24,356 --> 00:05:28,100 being challenging, okay. This is really important to remember, 89 00:05:28,100 --> 00:05:30,833 that big is relative. So let me give you a little bit of the 90 00:05:30,833 --> 00:05:34,658 history of the term big data. There's the earliest notion I could find 91 00:05:34,658 --> 00:05:37,178 was from Erik Larson in 1989 where he says, you know, the keepers of, from 92 00:05:37,178 --> 00:05:40,334 Harper's magazine that eventually went into a book. 93 00:05:40,334 --> 00:05:42,938 The keepers of Big Data say they do it for consumer's benefit but data have a 94 00:05:42,938 --> 00:05:46,290 way of being used for purposes other than originally intended. 95 00:05:46,290 --> 00:05:48,807 So his point was not really about technology at all. 96 00:05:48,807 --> 00:05:51,552 It was just a notion that data is being collected for one purpose and being 97 00:05:51,552 --> 00:05:54,529 reused for another. Which is a theme that I mentioned in the 98 00:05:54,529 --> 00:05:58,419 very first segment in this course and we'll come back to over and over again. 99 00:05:58,419 --> 00:06:01,530 And so I think he had it right that sense so his real point was that, you know 100 00:06:01,530 --> 00:06:05,437 about consumer private data starting to be commoditized. 101 00:06:05,437 --> 00:06:08,752 Which was absolutely, true and, and fairly prescient at the time since it's 102 00:06:08,752 --> 00:06:12,953 become a big issue now. But, you know, and it's been especially 103 00:06:12,953 --> 00:06:17,269 impressive that, you know, given that this predates the rise of the internet. 104 00:06:17,269 --> 00:06:20,686 and already sort of foreshadows very topical issues in big data, this ethics 105 00:06:20,686 --> 00:06:25,680 and privacy and sensitivity and so forth that we'll talk a little bit about. 106 00:06:25,680 --> 00:06:29,230 but this isn't quite what we mean by big data nowadays typically because it didn't 107 00:06:29,230 --> 00:06:33,662 have that technology aspect to it. It didn't talk about the challenge of 108 00:06:33,662 --> 00:06:37,149 actually managing this, these data sets alright. 109 00:06:37,149 --> 00:06:41,437 So another point of reference is that more reasonable reports from these 110 00:06:41,437 --> 00:06:45,390 consulting firms get credit for this notion of 3D's ,its got really the 111 00:06:45,390 --> 00:06:49,724 original source. This was a report from governor is 2001 112 00:06:49,724 --> 00:06:53,533 written by a guy named Doug Laney. And so we talked about volume, velocity 113 00:06:53,533 --> 00:06:56,557 and variety which we've said but let me just give you a chance to look at these 114 00:06:56,557 --> 00:06:59,537 quotes. You know and so in volume it's he's 115 00:06:59,537 --> 00:07:02,420 really talking about, sort of business to business. 116 00:07:02,420 --> 00:07:05,090 If you think about 2001, this is around the dot com boom. 117 00:07:05,090 --> 00:07:07,756 And so everyone was trying to figure out what this new era of technology was 118 00:07:07,756 --> 00:07:11,262 going to get, what the internet was really going to give to them beyond. 119 00:07:11,262 --> 00:07:14,370 Just, sort of putting up a webpage and serving it out to your customers. 120 00:07:14,370 --> 00:07:17,750 What, how are you going to be able to interact with your supply chain or your 121 00:07:17,750 --> 00:07:20,952 your vendors and so on. Okay, and so that's what it means by this 122 00:07:20,952 --> 00:07:23,736 notion of e-channels. But you know, up to ten x, the quantity 123 00:07:23,736 --> 00:07:27,470 of data about an individual transaction may be collected. 124 00:07:27,470 --> 00:07:30,462 You know, absolutely true that this data exhausts, this point we've made a couple 125 00:07:30,462 --> 00:07:34,680 of times, is giving rise to a larger scale of data being collected. 126 00:07:34,680 --> 00:07:37,452 You know, when velocity well has increased the point of interaction speed, 127 00:07:37,452 --> 00:07:40,850 right. So this is that need for interactivity. 128 00:07:40,850 --> 00:07:44,282 then but didn't used to be so required, but as the velocity of all business and 129 00:07:44,282 --> 00:07:48,357 all transactions sort of increased. So do the constraints on the 130 00:07:48,357 --> 00:07:52,510 infrastructure used to process it. And so on variety, I like this one a lot. 131 00:07:52,510 --> 00:07:55,978 Through 2003, 2004, right, so he's been sort of fairly conservative about how far 132 00:07:55,978 --> 00:07:59,649 out he wanted to predict. No greater barrier to effective data 133 00:07:59,649 --> 00:08:03,168 management will exist and the variety of incompatible data formats, non-aligned 134 00:08:03,168 --> 00:08:06,665 data structures and inconsistent data semantics. 135 00:08:06,665 --> 00:08:11,081 so this is great, this is, this is, you know, you could have said this for the 136 00:08:11,081 --> 00:08:17,269 through 2015 and been arguably correct, this problem is not gone away. 137 00:08:19,950 --> 00:08:23,183 So, another point in the history of this term Big Data there was a series of 138 00:08:23,183 --> 00:08:26,628 talks, a lot of work by John Mashey, who was formerly the chief scientist at the 139 00:08:26,628 --> 00:08:32,048 SGI, who would talk about Big Data being the next wave of infrastress. 140 00:08:32,048 --> 00:08:35,069 And so what he meant by infrastress was what's really going to drive the 141 00:08:35,069 --> 00:08:38,440 technology forward. Where we're going to feel the pain. 142 00:08:38,440 --> 00:08:42,444 And his point was that the IO interfaces, was where it was tough. 143 00:08:42,444 --> 00:08:46,272 So in particular disk, disk capacities were growing incredibly fast and still 144 00:08:46,272 --> 00:08:49,980 are and the latencies are not keeping pace, right. 145 00:08:49,980 --> 00:08:56,059 So you can go down to, a local store and buy 3-tier BI drive for probably $200. 146 00:08:57,600 --> 00:09:00,638 But the rate at which you can pull data off that is essentially the same as it 147 00:09:00,638 --> 00:09:04,877 has been for many, many year. And so now it takes you hours to actually 148 00:09:04,877 --> 00:09:09,360 read every byte of data on that disk that you're, that you stored. 149 00:09:09,360 --> 00:09:12,573 And so, this is a problem because the actual analysis you can do of all the 150 00:09:12,573 --> 00:09:16,988 data we can, you know we can keep it. And that's really cheap, but cannot do 151 00:09:16,988 --> 00:09:19,976 anything with it because the, the pipe is so small. 152 00:09:19,976 --> 00:09:23,432 Okay, and so, this, this is one of the argument, he made several sort of 153 00:09:23,432 --> 00:09:26,834 very[UNKNOWN] arguments about where the bottle necks are in, in, in the 154 00:09:26,834 --> 00:09:31,263 infrastructure. But they all sort of revolved around this 155 00:09:31,263 --> 00:09:34,719 idea that, that large, big, you know, big[UNKNOWN] processing were going to to 156 00:09:34,719 --> 00:09:38,692 be the a stress point. And so this is probably a pretty 157 00:09:38,692 --> 00:09:42,668 appropriate use of big data, although John Mashey has said, you know. 158 00:09:42,668 --> 00:09:46,256 That he doesn't, that he's not sure that he deserves any credit for coining this 159 00:09:46,256 --> 00:09:49,353 term, since it, it's a fairly generic term. 160 00:09:49,353 --> 00:09:52,681 and he, he was using it in one way, and we use it now in a, in a related way, but 161 00:09:52,681 --> 00:09:57,440 it's not necessarily that it captures everything we mean. 162 00:09:57,440 --> 00:10:01,655 Today, and I'd probably agree with him. Alright, so, just another quote about Big 163 00:10:01,655 --> 00:10:06,530 Data sort of today where we're trying capture exactly how it is being used. 164 00:10:06,530 --> 00:10:09,214 You know the necessity of grappling with Big Data and the desirability of 165 00:10:09,214 --> 00:10:13,300 unlocking information hidden within it, is now a key theme in all the sciences. 166 00:10:13,300 --> 00:10:16,490 And you know I like this, arguably the key scientific theme of our times. 167 00:10:16,490 --> 00:10:18,560 And so we talked about science, we talked about. 168 00:10:18,560 --> 00:10:21,458 The fact that I think what's going on in science is more or less equivalent to 169 00:10:21,458 --> 00:10:24,890 what's going on in business. And so I think this is, this is nice, 170 00:10:24,890 --> 00:10:27,440 right. This is really maybe the key problem 171 00:10:27,440 --> 00:10:31,588 across all fields, is, unlocking what's going on inside big data, right, getting 172 00:10:31,588 --> 00:10:35,580 something, extracting value out of Big Data. 173 00:10:35,580 --> 00:10:39,179 Right, so the final point I want to make is, you know, where does all this big 174 00:10:39,179 --> 00:10:42,579 data come from? And we said this a little bit before but 175 00:10:42,579 --> 00:10:44,995 one is dated exhaust from customers right. 176 00:10:44,995 --> 00:10:47,909 So were actually tracking a lot more information about interactions with 177 00:10:47,909 --> 00:10:50,917 customers than we used to right ts not just about taking there order its about 178 00:10:50,917 --> 00:10:55,670 monitoring there click stream that they use in order to get to that order. 179 00:10:55,670 --> 00:10:58,443 It's about not just about sending advertisements to them but its about 180 00:10:58,443 --> 00:11:01,409 watching how many clicks are on each advertisement. 181 00:11:01,409 --> 00:11:04,511 And whether the, the number of clicks goes up or down depending on where that 182 00:11:04,511 --> 00:11:08,430 ad is placed on the webpage, and so on. another point that, you know, especially 183 00:11:08,430 --> 00:11:10,635 true in science, but I think, is also true in business, and I'll give a couple 184 00:11:10,635 --> 00:11:12,490 examples of this, is that the availability of new and pervasive 185 00:11:12,490 --> 00:11:14,120 sensors. Right? 186 00:11:14,120 --> 00:11:17,480 We're actually able to get a, get visibility on data sources that we 187 00:11:17,480 --> 00:11:20,583 previously couldn't. And I'll give a couple examples of that 188 00:11:20,583 --> 00:11:23,438 in a second. And then I think, you know, I mentioned 189 00:11:23,438 --> 00:11:26,386 this already, but the side, the, the technology of data storage, right, just 190 00:11:26,386 --> 00:11:30,664 this capacities of disk has gone up. The cost of per storing a byte has gone 191 00:11:30,664 --> 00:11:34,120 down, and so we sort of have this ability to keep everything, whether or not we 192 00:11:34,120 --> 00:11:36,900 need it. Or at least there's a perceived ability 193 00:11:36,900 --> 00:11:39,826 to keep everything. Whether or not we need it, and so people 194 00:11:39,826 --> 00:11:42,268 are doing so right? There are things that they would have 195 00:11:42,268 --> 00:11:44,969 otherwise thrown away they are starting to keep. 196 00:11:44,969 --> 00:11:47,849 And then scratching their heads and thinking, boy how might I use this to 197 00:11:47,849 --> 00:11:51,070 make predictions and make better business decision? 198 00:11:51,070 --> 00:11:53,450 Okay. Okay, so just a couple of examples of 199 00:11:53,450 --> 00:11:56,248 sensors that may or may not lead to massive data. 200 00:11:56,248 --> 00:11:59,548 But just examples of where we are getting visibility on data sources that we did 201 00:11:59,548 --> 00:12:03,137 previously that we didn't have. So one is like, the fact that all new 202 00:12:03,137 --> 00:12:05,803 cars are going to be equipped with these black boxes that are a lot like what's 203 00:12:05,803 --> 00:12:09,160 going on inside air, what, what airliners have. 204 00:12:09,160 --> 00:12:12,040 And you know, the reason is for forensics in the event of a crash, but they also 205 00:12:12,040 --> 00:12:16,042 record a lot of other information. And so insurance companies have similar 206 00:12:16,042 --> 00:12:19,114 devices that you can opt, you can opt in, you can voluntarily plug in to reduce 207 00:12:19,114 --> 00:12:22,999 your insurance rates. That track your speed, track other kinds 208 00:12:22,999 --> 00:12:27,690 of aspects of your driving habits. So, this technology would have been 209 00:12:27,690 --> 00:12:31,010 simply hard to imagine in you know, 20 or 30 years ago. 210 00:12:31,010 --> 00:12:33,489 But, now that we have the technology, why not actually start collecting the data 211 00:12:33,489 --> 00:12:35,110 from it. Okay. 212 00:12:35,110 --> 00:12:37,510 And, so while the purpose here is pretty clear at least for the insurance 213 00:12:37,510 --> 00:12:40,367 companies and for these black boxes for crash forensics. 214 00:12:40,367 --> 00:12:42,967 You can imagine re-purposing that data for other purposes, and like that this 215 00:12:42,967 --> 00:12:45,487 article is about was well boy, you know is, is there privacy risk here, given 216 00:12:45,487 --> 00:12:47,927 that there's one purpose, you that, they are being deployed for crash for 217 00:12:47,927 --> 00:12:51,145 instance. But they might be used of or other 218 00:12:51,145 --> 00:12:53,750 purposes. And for insurance companies you can 219 00:12:53,750 --> 00:12:57,440 imagine how they would collect it with a particular. 220 00:12:57,440 --> 00:13:00,128 Actuarial risk modeling mind, but maybe they'll develop other models in the 221 00:13:00,128 --> 00:13:02,547 future, given that now they have this data. 222 00:13:02,547 --> 00:13:04,064 Okay. And so I think this is really a theme of 223 00:13:04,064 --> 00:13:06,752 Big Data is that we're collecting new sources of information independent of 224 00:13:06,752 --> 00:13:10,275 whether we know how we're going to use them in the future. 225 00:13:10,275 --> 00:13:12,078 Okay. So let me give you another couple of 226 00:13:12,078 --> 00:13:15,735 examples from research here by Shwetak Patel in the computer science engineering 227 00:13:15,735 --> 00:13:19,264 department. And there are several related devices and 228 00:13:19,264 --> 00:13:23,020 here I just mentioned two of them, HydroSense and ElectriSense. 229 00:13:23,020 --> 00:13:27,229 And so, both of these devices are intended for consumers to use to monitor 230 00:13:27,229 --> 00:13:31,690 their own resource consumption. And so, instead of having to, kind of, 231 00:13:31,690 --> 00:13:34,090 rewire your house to monitor your, monitoring the consumption of every 232 00:13:34,090 --> 00:13:37,330 device in your house, every faucet, every shower. 233 00:13:37,330 --> 00:13:39,967 And so on. You can just clamp this device sort of on 234 00:13:39,967 --> 00:13:43,625 the main water line coming into your house and it will monitor the pressure 235 00:13:43,625 --> 00:13:48,250 changes associate with every individual device. 236 00:13:48,250 --> 00:13:51,220 So it can disambiguate that flow and recognize the signature that every device 237 00:13:51,220 --> 00:13:54,441 puts on the pressure changes. So every time you turn on the shower in 238 00:13:54,441 --> 00:13:57,759 the upstairs bathroom, or flush the toilet in the downstairs bathroom. 239 00:13:57,759 --> 00:14:00,301 This thing can tell you, can identify when that happens and give you a log of 240 00:14:00,301 --> 00:14:03,914 the events. And by analyzing that log, you can tell 241 00:14:03,914 --> 00:14:08,135 you know, where, which device, where most of your water is going. 242 00:14:08,135 --> 00:14:12,535 Is it mostly going for showers, is it mostly going for dishwasher and so on. 243 00:14:12,535 --> 00:14:17,975 ElectriSense is very similar, in that every electrical device in your house 244 00:14:17,975 --> 00:14:22,115 puts a. Recognizable load on the signal on the 245 00:14:22,115 --> 00:14:26,015 power signal that can be read and disambiguated to tell you where, where 246 00:14:26,015 --> 00:14:29,190 your energy is going. Okay. 247 00:14:29,190 --> 00:14:32,410 So these are just examples of new sensors that are coming on the market where data 248 00:14:32,410 --> 00:14:36,850 is being derived, that otherwise wouldn't of been able to be derived at all.