1 00:00:00,090 --> 00:00:02,490 The following content is provided under a Creative 2 00:00:02,490 --> 00:00:04,030 Commons license. 3 00:00:04,030 --> 00:00:06,330 Your support will help MIT OpenCourseWare 4 00:00:06,330 --> 00:00:10,720 continue to offer high-quality educational resources for free. 5 00:00:10,720 --> 00:00:13,320 To make a donation or view additional materials 6 00:00:13,320 --> 00:00:17,280 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,280 --> 00:00:19,550 at ocw.mit.edu. 8 00:00:19,550 --> 00:00:21,300 MARK HARTMAN: So we're going to put down-- 9 00:00:21,300 --> 00:00:22,925 we're going to talk together about what 10 00:00:22,925 --> 00:00:33,870 is the point of the restaurant analogy. 11 00:00:33,870 --> 00:00:34,950 What is an analogy? 12 00:00:38,240 --> 00:00:41,900 Anybody remember what an analogy is? 13 00:00:41,900 --> 00:00:43,310 Chris, you remember what it is. 14 00:00:43,310 --> 00:00:43,820 So tell us. 15 00:00:43,820 --> 00:00:44,782 AUDIENCE: Oh, wait. 16 00:00:44,782 --> 00:00:47,190 Is it like [INAUDIBLE]? 17 00:00:47,190 --> 00:00:48,009 MARK HARTMAN: No. 18 00:00:48,009 --> 00:00:48,550 AUDIENCE: Oh. 19 00:00:48,550 --> 00:00:49,550 Wait, no. 20 00:00:49,550 --> 00:00:50,790 MARK HARTMAN: An analogy. 21 00:00:50,790 --> 00:00:53,870 Think back to English class. 22 00:00:53,870 --> 00:00:57,390 Lauren knows, so she's going to tell us. 23 00:00:57,390 --> 00:00:57,890 Ooh. 24 00:00:57,890 --> 00:01:00,160 AUDIENCE: Well, I don't really know how to explain it. 25 00:01:00,160 --> 00:01:03,164 But it's when you take one situation 26 00:01:03,164 --> 00:01:05,519 and you relate it to another. 27 00:01:05,519 --> 00:01:07,560 MARK HARTMAN: OK, when you take one situation 28 00:01:07,560 --> 00:01:08,910 and you relate it to another. 29 00:01:08,910 --> 00:01:10,130 AUDIENCE: You compare. 30 00:01:10,130 --> 00:01:11,130 MARK HARTMAN: Like what? 31 00:01:11,130 --> 00:01:12,150 AUDIENCE: You compare. 32 00:01:12,150 --> 00:01:13,233 MARK HARTMAN: You compare. 33 00:01:13,233 --> 00:01:14,910 You compare two things. 34 00:01:14,910 --> 00:01:18,700 An analogy would be like-- 35 00:01:18,700 --> 00:01:22,020 ugh, I can't come up with one off the top of my head. 36 00:01:22,020 --> 00:01:30,420 So fruit is to apple as zucchini is to vegetable. 37 00:01:30,420 --> 00:01:32,680 An apple is a specific kind of fruit, 38 00:01:32,680 --> 00:01:34,400 so there's a relationship there. 39 00:01:34,400 --> 00:01:36,654 But a zucchini is also a specific kind of vegetable. 40 00:01:36,654 --> 00:01:38,820 I heard you guys talking about fruits and vegetables 41 00:01:38,820 --> 00:01:41,250 out in the hallway before. 42 00:01:41,250 --> 00:01:44,820 So an analogy is a way to draw a parallel 43 00:01:44,820 --> 00:01:49,170 or draw a connection between two situations that seem different, 44 00:01:49,170 --> 00:01:52,015 but there's some part of that situation that's the same. 45 00:01:52,015 --> 00:01:53,640 And that's what we're going to at here. 46 00:01:53,640 --> 00:01:56,040 We're going to make three columns here, 47 00:01:56,040 --> 00:01:58,740 and we're going to compare the restaurant. 48 00:02:02,250 --> 00:02:05,040 We're also going to compare-- 49 00:02:05,040 --> 00:02:08,759 let's say this is our restaurant data. 50 00:02:08,759 --> 00:02:13,200 Or I'm sorry, restaurant observation. 51 00:02:16,480 --> 00:02:21,380 Then we're going to look at an astronomical observation. 52 00:02:24,940 --> 00:02:27,820 And then we're going to look at what it's called, or the name. 53 00:02:32,980 --> 00:02:36,590 So leave a good amount of space underneath this. 54 00:02:36,590 --> 00:02:40,490 You need at least a half a page, if not more. 55 00:02:44,560 --> 00:02:48,000 So the first restaurant observation that we made 56 00:02:48,000 --> 00:02:54,000 was this histogram, and it was a histogram of the number 57 00:02:54,000 --> 00:03:01,890 of people polled-- 58 00:03:01,890 --> 00:03:06,080 does everybody know what a poll is, P-O-L-L? 59 00:03:06,080 --> 00:03:08,270 If you've ever heard of an election poll, that's 60 00:03:08,270 --> 00:03:11,900 when people stand outside of the election booth and they say, 61 00:03:11,900 --> 00:03:13,850 will you tell us who you voted for? 62 00:03:13,850 --> 00:03:15,050 You don't have to tell them. 63 00:03:15,050 --> 00:03:20,210 But it's the number of people polled or asked 64 00:03:20,210 --> 00:03:28,600 leaving the restaurant, the number of people 65 00:03:28,600 --> 00:03:32,470 polled leaving the restaurant. 66 00:03:32,470 --> 00:03:35,260 And we made a histogram. 67 00:03:35,260 --> 00:03:38,320 That was the y-axis. 68 00:03:38,320 --> 00:03:44,980 And we said, how many calories were carried out? 69 00:03:47,370 --> 00:03:49,620 Because we asked them, how many calories did you have? 70 00:03:49,620 --> 00:03:55,240 And we saw that there were some peaks that were low, 71 00:03:55,240 --> 00:03:56,460 maybe went down. 72 00:03:56,460 --> 00:03:58,710 And then there was a good amount that 73 00:03:58,710 --> 00:04:00,930 were out here at high calories. 74 00:04:00,930 --> 00:04:06,420 So we saw, yeah, there was some peak at low, also 75 00:04:06,420 --> 00:04:09,116 some peak at high. 76 00:04:09,116 --> 00:04:11,586 AUDIENCE: What's that say? 77 00:04:11,586 --> 00:04:13,480 MARK HARTMAN: It says, number of people 78 00:04:13,480 --> 00:04:14,779 polled leaving the restaurant. 79 00:04:14,779 --> 00:04:15,529 AUDIENCE: Oh, yes. 80 00:04:15,529 --> 00:04:16,329 Thank you. 81 00:04:16,329 --> 00:04:16,829 MARK HARTMAN: Or if you don't want 82 00:04:16,829 --> 00:04:19,329 to use "polled," you could just say, number of people asked. 83 00:04:24,864 --> 00:04:26,530 These people came out of the restaurant. 84 00:04:26,530 --> 00:04:28,946 We stopped them and said, hey, how much food did you have? 85 00:04:33,560 --> 00:04:35,240 We also, just today-- 86 00:04:35,240 --> 00:04:38,210 so down below-- we made another histogram. 87 00:04:38,210 --> 00:04:43,910 And again, it was the number of people 88 00:04:43,910 --> 00:04:47,811 asked leaving the restaurant. 89 00:04:53,703 --> 00:04:56,320 But what was our x-axis this time? 90 00:04:56,320 --> 00:04:59,572 We asked them about the number of calories that they ate, 91 00:04:59,572 --> 00:05:01,030 but what did we ask them this time? 92 00:05:01,030 --> 00:05:01,705 AUDIENCE: Time. 93 00:05:01,705 --> 00:05:02,830 The time they left. 94 00:05:02,830 --> 00:05:04,840 MARK HARTMAN: We asked them what time is it. 95 00:05:04,840 --> 00:05:07,160 What time did you leave the restaurant? 96 00:05:07,160 --> 00:05:12,985 So we're going to say, time the person left. 97 00:05:17,580 --> 00:05:21,540 And we found that there was kind of a peak here at low times, 98 00:05:21,540 --> 00:05:22,655 at 8:00 AM. 99 00:05:22,655 --> 00:05:25,890 And then there was kind of another peak here at lunch. 100 00:05:25,890 --> 00:05:31,505 And then there was another wider peak at dinnertime. 101 00:05:43,120 --> 00:05:45,280 So those are two observations that we 102 00:05:45,280 --> 00:05:48,400 made about the people who were leaving our restaurant. 103 00:05:48,400 --> 00:05:52,870 Well, it's not our restaurant, but somebody's restaurant. 104 00:05:52,870 --> 00:05:55,420 What is an astronomical observation 105 00:05:55,420 --> 00:05:59,060 that's kind of like the first observation? 106 00:05:59,060 --> 00:06:02,500 Instead of the number of people asked leaving the restaurant, 107 00:06:02,500 --> 00:06:10,000 let's look at the number of photons 108 00:06:10,000 --> 00:06:13,420 collected at the detector. 109 00:06:20,790 --> 00:06:23,630 We've made histograms like that before, right-- 110 00:06:23,630 --> 00:06:25,390 the number of photons collected. 111 00:06:25,390 --> 00:06:26,390 But what was our x-axis? 112 00:06:30,247 --> 00:06:30,746 It was? 113 00:06:30,746 --> 00:06:31,132 AUDIENCE: Energy. 114 00:06:31,132 --> 00:06:32,400 MARK HARTMAN: It was energy. 115 00:06:32,400 --> 00:06:34,080 We looked at the energy of each photon. 116 00:06:44,450 --> 00:06:45,440 What did we call-- 117 00:06:45,440 --> 00:06:50,840 and let's look at the supernova remnant spectrum. 118 00:06:50,840 --> 00:06:52,550 It kind of looked like this. 119 00:06:52,550 --> 00:06:54,530 It kind of went up. 120 00:06:54,530 --> 00:06:56,900 There was a spike, a couple of spikes, 121 00:06:56,900 --> 00:06:59,480 and then maybe a couple of other peaks. 122 00:06:59,480 --> 00:07:02,060 And we found out that each one of those peaks 123 00:07:02,060 --> 00:07:07,040 was produced by an element that was giving off 124 00:07:07,040 --> 00:07:10,760 a particular energy of photon because it was bounced around. 125 00:07:16,724 --> 00:07:19,780 So let's think about this analogy. 126 00:07:19,780 --> 00:07:22,670 Here, we've got the number of things collected. 127 00:07:22,670 --> 00:07:25,330 Here, we've got the number of people collected, 128 00:07:25,330 --> 00:07:27,340 the number of people asked. 129 00:07:27,340 --> 00:07:30,070 Here, we've got the energy of each photon. 130 00:07:30,070 --> 00:07:33,130 Over here, we've got the energy that the people carried out. 131 00:07:33,130 --> 00:07:34,880 Calories is a measurement of energy. 132 00:07:34,880 --> 00:07:36,385 How much food did they have? 133 00:07:36,385 --> 00:07:38,380 That kind of makes sense. 134 00:07:38,380 --> 00:07:39,725 What did we call this graph? 135 00:07:44,360 --> 00:07:46,509 What was the name of this observation 136 00:07:46,509 --> 00:07:48,050 if we looked at the number of photons 137 00:07:48,050 --> 00:07:53,761 collected as a function, or on the x-axis, as energy? 138 00:07:53,761 --> 00:07:54,260 David? 139 00:07:54,260 --> 00:07:55,887 AUDIENCE: A spectrum analysis. 140 00:07:55,887 --> 00:07:57,470 MARK HARTMAN: We called it a spectrum. 141 00:07:57,470 --> 00:07:59,747 When we did an analysis of it, we looked at it 142 00:07:59,747 --> 00:08:01,080 and compared it to other things. 143 00:08:01,080 --> 00:08:06,550 But we called this a spectrum. 144 00:08:06,550 --> 00:08:11,830 And we said a spectrum represents the intensity 145 00:08:11,830 --> 00:08:12,950 as a function of energy. 146 00:08:12,950 --> 00:08:19,276 We could also call this number of photons collected intensity. 147 00:08:22,610 --> 00:08:26,240 Well, we're going to learn, very quickly, how we can 148 00:08:26,240 --> 00:08:31,790 do something similar with time. 149 00:08:31,790 --> 00:08:34,659 Again, we're going to look at an astronomical observation. 150 00:08:34,659 --> 00:08:42,740 And again, we're going to say, the number of photons 151 00:08:42,740 --> 00:08:45,530 collected at the detector. 152 00:08:50,484 --> 00:08:52,400 Actually, I'm going to add in one other thing. 153 00:08:52,400 --> 00:08:54,200 Here, we said the number of photons 154 00:08:54,200 --> 00:08:55,850 collected at the detector. 155 00:08:55,850 --> 00:09:02,360 We're going to say the number of photons of one color 156 00:09:02,360 --> 00:09:05,530 because we said, for intensity, we 157 00:09:05,530 --> 00:09:08,350 had to specify that it was a certain energy of photon 158 00:09:08,350 --> 00:09:09,660 or a certain color of photon. 159 00:09:11,857 --> 00:09:14,190 Well, here, we're going to look at the number of photons 160 00:09:14,190 --> 00:09:15,273 collected at the detector. 161 00:09:18,500 --> 00:09:21,670 How could we draw the analogy between our situations now? 162 00:09:21,670 --> 00:09:24,160 What should we put on the x-axis for 163 00:09:24,160 --> 00:09:26,538 our astronomical observation? 164 00:09:26,538 --> 00:09:31,065 AUDIENCE: The time that [INAUDIBLE] by the detector. 165 00:09:31,065 --> 00:09:33,440 MARK HARTMAN: OK, say it nice and loud to everybody else. 166 00:09:33,440 --> 00:09:37,482 AUDIENCE: The time that the shot was taken by the detector. 167 00:09:37,482 --> 00:09:38,190 MARK HARTMAN: OK. 168 00:09:38,190 --> 00:09:41,510 We are going to say the time each photon was collected 169 00:09:41,510 --> 00:09:54,980 by the detector, time each photon was collected 170 00:09:54,980 --> 00:09:55,665 by the detector. 171 00:10:01,889 --> 00:10:03,180 And again, it's going to look-- 172 00:10:05,910 --> 00:10:08,867 well, we actually don't know because you 173 00:10:08,867 --> 00:10:09,700 haven't done it yet. 174 00:10:09,700 --> 00:10:10,366 You're about to. 175 00:10:17,950 --> 00:10:20,417 Now, we are going to say that in this case, 176 00:10:20,417 --> 00:10:22,000 we're looking at the number of photons 177 00:10:22,000 --> 00:10:23,590 collected at the detector. 178 00:10:23,590 --> 00:10:27,550 We don't care about what energy they are just yet. 179 00:10:27,550 --> 00:10:33,070 So this is again going to be flux. 180 00:10:33,070 --> 00:10:36,010 It's just the number of photons that we collected. 181 00:10:36,010 --> 00:10:38,140 Remember, we said before when we're 182 00:10:38,140 --> 00:10:39,670 looking at variable sources, we want 183 00:10:39,670 --> 00:10:42,430 to look at the amount of the flux change. 184 00:10:42,430 --> 00:10:45,479 We also look at the time that it took for the flux to change. 185 00:10:45,479 --> 00:10:46,270 Well, look at that. 186 00:10:46,270 --> 00:10:48,603 On this graph, we've got one axis for each one of those. 187 00:10:48,603 --> 00:10:49,280 How about that? 188 00:10:56,770 --> 00:10:59,890 We're going to call this observation or this kind 189 00:10:59,890 --> 00:11:08,730 of observation a light curve. 190 00:11:08,730 --> 00:11:12,300 We should really call it a flux histogram, 191 00:11:12,300 --> 00:11:15,810 but historically, people have called it a light curve. 192 00:11:15,810 --> 00:11:17,430 It's the amount of photons collected 193 00:11:17,430 --> 00:11:22,100 at the detector, the flux, as a function of time.