WEBVTT 00:00:00.000 --> 00:00:02.964 align:middle line:84% [SQUEAKING] [RUSTLING] [CLICKING] 00:00:02.964 --> 00:00:11.380 align:middle line:90% 00:00:11.380 --> 00:00:12.770 align:middle line:90% DAVID KAISER: Hi, everyone. 00:00:12.770 --> 00:00:17.950 align:middle line:90% Welcome back to 8225 STS 042. 00:00:17.950 --> 00:00:20.510 align:middle line:84% Any questions on, again, any kind of logistical stuff? 00:00:20.510 --> 00:00:24.850 align:middle line:90% 00:00:24.850 --> 00:00:27.280 align:middle line:84% If not, then I think we'll jump right in. 00:00:27.280 --> 00:00:29.170 align:middle line:84% So I'm going to go ahead and share screen. 00:00:29.170 --> 00:00:34.940 align:middle line:84% I'm eager to get into this next set of material together. 00:00:34.940 --> 00:00:38.950 align:middle line:84% So hopefully, you now see my shared screen. 00:00:38.950 --> 00:00:42.070 align:middle line:84% Nods or thumbs up, just to confirm? 00:00:42.070 --> 00:00:42.612 align:middle line:90% Looking good. 00:00:42.612 --> 00:00:43.320 align:middle line:90% Thanks, everyone. 00:00:43.320 --> 00:00:43.900 align:middle line:90% OK, great. 00:00:43.900 --> 00:00:47.200 align:middle line:84% So today's lecture is still going 00:00:47.200 --> 00:00:50.930 align:middle line:84% to be situated pretty squarely in the late 19th century. 00:00:50.930 --> 00:00:53.200 align:middle line:84% We're going to pick up from where we were 00:00:53.200 --> 00:00:57.380 align:middle line:90% during the previous discussion. 00:00:57.380 --> 00:01:01.270 align:middle line:84% So as a reminder, the lecture today-- actually, 00:01:01.270 --> 00:01:02.950 align:middle line:90% unusual for me-- has four parts. 00:01:02.950 --> 00:01:04.840 align:middle line:84% Usually, my lectures have three parts. 00:01:04.840 --> 00:01:06.760 align:middle line:84% These will be four a little bit shorter parts. 00:01:06.760 --> 00:01:08.802 align:middle line:84% And we'll break for some questions and discussion 00:01:08.802 --> 00:01:10.870 align:middle line:90% between each of these. 00:01:10.870 --> 00:01:14.390 align:middle line:84% Quick recap though of where we were last time-- 00:01:14.390 --> 00:01:18.430 align:middle line:84% so in the previous lecture, we looked at a few exemplars, 00:01:18.430 --> 00:01:21.610 align:middle line:84% pretty telling examples of the kinds of work 00:01:21.610 --> 00:01:25.000 align:middle line:84% that was coming together in the middle and late 19th century-- 00:01:25.000 --> 00:01:28.000 align:middle line:84% in that case, largely in Britain. 00:01:28.000 --> 00:01:30.820 align:middle line:84% We looked at people like Michael Faraday. 00:01:30.820 --> 00:01:35.480 align:middle line:84% Faraday is fascinating for his personal story, his biography, 00:01:35.480 --> 00:01:38.540 align:middle line:84% but also for what he indicates in terms 00:01:38.540 --> 00:01:40.820 align:middle line:84% of what were the pressing questions 00:01:40.820 --> 00:01:43.910 align:middle line:84% for natural researchers in his day and what were the kinds 00:01:43.910 --> 00:01:45.290 align:middle line:90% of institutional arrangements. 00:01:45.290 --> 00:01:48.200 align:middle line:84% Where did he think it would make sense to get his work done? 00:01:48.200 --> 00:01:50.990 align:middle line:84% So we saw that he had very little formal education. 00:01:50.990 --> 00:01:54.890 align:middle line:84% He was apprenticed at around age 13 to a bookbinder, 00:01:54.890 --> 00:01:57.020 align:middle line:84% and then later basically apprenticed 00:01:57.020 --> 00:02:00.050 align:middle line:84% in a new kind of position as a natural philosopher 00:02:00.050 --> 00:02:01.610 align:middle line:84% at this special kind of place called 00:02:01.610 --> 00:02:03.750 align:middle line:84% the Royal Institution, which, remember, 00:02:03.750 --> 00:02:05.810 align:middle line:90% was not a school or university. 00:02:05.810 --> 00:02:07.880 align:middle line:84% It did not have students enrolled. 00:02:07.880 --> 00:02:11.780 align:middle line:84% It was a place that fostered research and also 00:02:11.780 --> 00:02:14.390 align:middle line:84% a lot of what we might today call public outreach, 00:02:14.390 --> 00:02:16.890 align:middle line:90% public lectures, and so on. 00:02:16.890 --> 00:02:19.460 align:middle line:84% So in Faraday's own case, we know 00:02:19.460 --> 00:02:22.280 align:middle line:84% he had many reasons to dig into the topics 00:02:22.280 --> 00:02:25.058 align:middle line:84% that he wound up studying throughout his life, one 00:02:25.058 --> 00:02:27.350 align:middle line:84% of which seems to have been inspired, at least in part, 00:02:27.350 --> 00:02:30.020 align:middle line:90% by his unusual religious faith. 00:02:30.020 --> 00:02:32.090 align:middle line:84% Remember, he was a Protestant, as we 00:02:32.090 --> 00:02:35.270 align:middle line:84% talked about last time, but not an Anglican, not a member 00:02:35.270 --> 00:02:37.070 align:middle line:84% of the official church of England. 00:02:37.070 --> 00:02:40.670 align:middle line:84% And so his Protestant sect was particularly 00:02:40.670 --> 00:02:44.090 align:middle line:84% fascinated by this interconversion, an underlying 00:02:44.090 --> 00:02:45.830 align:middle line:90% unity of nature. 00:02:45.830 --> 00:02:49.070 align:middle line:84% And for Faraday, that reinforced an interest for him 00:02:49.070 --> 00:02:52.430 align:middle line:84% in studying how physical forces could change one 00:02:52.430 --> 00:02:54.710 align:middle line:84% into the other or different kinds of effects 00:02:54.710 --> 00:02:57.470 align:middle line:84% could impact each other-- electric and magnetic, 00:02:57.470 --> 00:03:01.260 align:middle line:84% electrolysis and chemical interactions, and so on. 00:03:01.260 --> 00:03:04.820 align:middle line:84% Now, as far as Faraday and really his entire generation 00:03:04.820 --> 00:03:08.960 align:middle line:84% was concerned, all of these interconvertible effects, 00:03:08.960 --> 00:03:12.620 align:middle line:84% all of these physical forces, were made possible 00:03:12.620 --> 00:03:16.330 align:middle line:84% because they were all seated in this all pervasive luminiferous 00:03:16.330 --> 00:03:16.830 align:middle line:90% ether. 00:03:16.830 --> 00:03:18.470 align:middle line:84% We looked at this word last time. 00:03:18.470 --> 00:03:20.180 align:middle line:90% It's a great word-- 00:03:20.180 --> 00:03:22.910 align:middle line:84% lumen- coming from the Latin meaning light 00:03:22.910 --> 00:03:25.730 align:middle line:84% and -ferous meaning to carry, the light-bearing 00:03:25.730 --> 00:03:28.070 align:middle line:90% or light-carrying ether. 00:03:28.070 --> 00:03:30.020 align:middle line:84% So in the course of his investigations 00:03:30.020 --> 00:03:33.800 align:middle line:84% of this all pervasive, mechanical, elastic medium 00:03:33.800 --> 00:03:37.790 align:middle line:84% of the ether, Faraday introduced lines of force, 00:03:37.790 --> 00:03:41.670 align:middle line:84% and then developed from that this idea of fields, 00:03:41.670 --> 00:03:43.580 align:middle line:84% these fields that would characterize, 00:03:43.580 --> 00:03:47.630 align:middle line:84% as far as Faraday, was concerned the local state of the ether. 00:03:47.630 --> 00:03:49.850 align:middle line:84% What were the stresses, or strains, 00:03:49.850 --> 00:03:54.980 align:middle line:84% or tensions in that elastic, bendable, flexible medium 00:03:54.980 --> 00:03:58.490 align:middle line:84% in this location at this time, in some other location 00:03:58.490 --> 00:04:02.040 align:middle line:84% at that time, at the first location at some later time? 00:04:02.040 --> 00:04:04.010 align:middle line:84% And so he introduced this notion of fields 00:04:04.010 --> 00:04:08.070 align:middle line:84% to help make sense of the underlying state of the ether. 00:04:08.070 --> 00:04:11.000 align:middle line:84% And so instead of having this action at a distance, 00:04:11.000 --> 00:04:13.160 align:middle line:84% he was really emphasizing local effects. 00:04:13.160 --> 00:04:15.840 align:middle line:84% Local causes lead to local effects. 00:04:15.840 --> 00:04:17.690 align:middle line:84% And this is what we would now consider 00:04:17.690 --> 00:04:19.680 align:middle line:90% the birth of field theory. 00:04:19.680 --> 00:04:23.690 align:middle line:84% We use field theory all the time across physics, more than ever. 00:04:23.690 --> 00:04:27.080 align:middle line:84% It's coming really from work by people like Faraday, 00:04:27.080 --> 00:04:30.980 align:middle line:84% in their mind, to understand this particular, physical, real 00:04:30.980 --> 00:04:33.200 align:middle line:84% substance that filled the whole universe, 00:04:33.200 --> 00:04:35.310 align:middle line:84% as far as they were concerned, the ether. 00:04:35.310 --> 00:04:35.810 align:middle line:90% OK. 00:04:35.810 --> 00:04:40.050 align:middle line:90% Then we looked last time at-- 00:04:40.050 --> 00:04:40.890 align:middle line:90% whoops, let's see. 00:04:40.890 --> 00:04:41.490 align:middle line:90% There we go. 00:04:41.490 --> 00:04:42.907 align:middle line:84% We looked at some of the folks who 00:04:42.907 --> 00:04:45.720 align:middle line:84% were coming downstream from Faraday, 00:04:45.720 --> 00:04:48.580 align:middle line:84% people like William Thomson, later Lord Kelvin, 00:04:48.580 --> 00:04:49.980 align:middle line:90% and James Clerk Maxwell. 00:04:49.980 --> 00:04:52.230 align:middle line:84% So they shared Faraday's fascination 00:04:52.230 --> 00:04:54.300 align:middle line:84% with electrical and magnetic effects. 00:04:54.300 --> 00:04:56.640 align:middle line:84% They shared Faraday's fascination 00:04:56.640 --> 00:04:58.410 align:middle line:90% with all pervasive ether. 00:04:58.410 --> 00:05:02.220 align:middle line:84% They began to approach those questions with a somewhat 00:05:02.220 --> 00:05:03.480 align:middle line:90% different toolkit. 00:05:03.480 --> 00:05:06.690 align:middle line:84% So unlike Faraday, who had very little formal schooling 00:05:06.690 --> 00:05:10.020 align:middle line:84% beyond something like early middle school or junior high, 00:05:10.020 --> 00:05:13.350 align:middle line:84% Thompson and Maxwell became early graduates 00:05:13.350 --> 00:05:17.430 align:middle line:84% of this really new, fast-changing system 00:05:17.430 --> 00:05:19.560 align:middle line:84% centered largely at Cambridge University, 00:05:19.560 --> 00:05:21.430 align:middle line:84% but quickly became common elsewhere. 00:05:21.430 --> 00:05:24.090 align:middle line:84% So by the middle decades of the 19th century, 00:05:24.090 --> 00:05:27.510 align:middle line:84% Thompson and Maxwell were approaching Faraday-type 00:05:27.510 --> 00:05:30.360 align:middle line:84% questions, but with a new set of tools-- 00:05:30.360 --> 00:05:32.940 align:middle line:84% highly mathematical, highly formal tools. 00:05:32.940 --> 00:05:36.720 align:middle line:84% And they were both fascinated by these mathematical analogies 00:05:36.720 --> 00:05:40.030 align:middle line:84% between electromagnetic phenomena and mechanics. 00:05:40.030 --> 00:05:41.890 align:middle line:84% And in fact, they articulated what we 00:05:41.890 --> 00:05:43.830 align:middle line:90% call the mechanical worldview. 00:05:43.830 --> 00:05:46.090 align:middle line:84% We'll see more examples of that today. 00:05:46.090 --> 00:05:49.390 align:middle line:84% It was in the context of exactly that kind of study, 00:05:49.390 --> 00:05:51.220 align:middle line:84% in part because of the importance 00:05:51.220 --> 00:05:56.080 align:middle line:84% of things like telegraphy to the emerging British empire-- 00:05:56.080 --> 00:05:58.090 align:middle line:84% it was within that context that Maxwell 00:05:58.090 --> 00:06:00.670 align:middle line:84% was studying the way in which an all 00:06:00.670 --> 00:06:04.450 align:middle line:84% pervasive light-bearing ether would respond 00:06:04.450 --> 00:06:06.520 align:middle line:90% to kinds of disturbances. 00:06:06.520 --> 00:06:10.180 align:middle line:84% You tweak the ether here, how would that disturbance travel 00:06:10.180 --> 00:06:11.920 align:middle line:90% or spread throughout the ether. 00:06:11.920 --> 00:06:13.780 align:middle line:84% And he came to the conclusion, as we 00:06:13.780 --> 00:06:15.760 align:middle line:84% saw at the very end of the previous lecture, 00:06:15.760 --> 00:06:19.000 align:middle line:84% that light was actually not related to but was, 00:06:19.000 --> 00:06:23.290 align:middle line:84% in fact, nothing other than these transverse undulations, 00:06:23.290 --> 00:06:27.010 align:middle line:84% a certain kind of wave of disturbance within the ether. 00:06:27.010 --> 00:06:29.350 align:middle line:84% The light, in particular, were waves 00:06:29.350 --> 00:06:32.530 align:middle line:84% of electric and magnetic fields as they 00:06:32.530 --> 00:06:35.950 align:middle line:84% propagated in that kind of mechanical elastic. 00:06:35.950 --> 00:06:39.220 align:middle line:84% That was just to get us back up to speed from where we were 00:06:39.220 --> 00:06:41.396 align:middle line:90% in the previous discussion. 00:06:41.396 --> 00:06:43.750 align:middle line:84% So now, I want to talk about Maxwell's equations. 00:06:43.750 --> 00:06:46.270 align:middle line:84% In some sense, we know Maxwell's equations really well. 00:06:46.270 --> 00:06:48.280 align:middle line:84% We still learn them in high school, and college, 00:06:48.280 --> 00:06:49.113 align:middle line:90% and graduate school. 00:06:49.113 --> 00:06:51.070 align:middle line:90% They're incredibly important. 00:06:51.070 --> 00:06:54.400 align:middle line:84% But the way we manipulate them, how we actually 00:06:54.400 --> 00:06:56.080 align:middle line:90% handle these equations is-- 00:06:56.080 --> 00:06:57.910 align:middle line:84% I would say thank goodness-- pretty 00:06:57.910 --> 00:07:00.730 align:middle line:84% different from how Maxwell or Maxwell's immediate circle 00:07:00.730 --> 00:07:01.790 align:middle line:90% handled them. 00:07:01.790 --> 00:07:05.410 align:middle line:84% So a lot of Maxwell's work that we remember and make 00:07:05.410 --> 00:07:08.230 align:middle line:84% most use of were results that he was working out 00:07:08.230 --> 00:07:12.190 align:middle line:84% in the 1850s and 1860s, pretty early in his career. 00:07:12.190 --> 00:07:15.430 align:middle line:84% As we saw briefly last time, he bundled all those results 00:07:15.430 --> 00:07:19.690 align:middle line:84% together in a very massive, two-volume book published 00:07:19.690 --> 00:07:25.300 align:middle line:84% in 1873, totaling about 900 pages between the two volumes 00:07:25.300 --> 00:07:28.150 align:middle line:84% called the Treatise on Electricity and Magnetism. 00:07:28.150 --> 00:07:30.610 align:middle line:84% And in there is where he lays out 00:07:30.610 --> 00:07:34.690 align:middle line:84% a first principle description of electricity magnetism 00:07:34.690 --> 00:07:36.880 align:middle line:84% and even much of optics, given the fact 00:07:36.880 --> 00:07:39.010 align:middle line:84% that he had figured out or argued 00:07:39.010 --> 00:07:41.890 align:middle line:84% that light was nothing other than electromagnetic effects 00:07:41.890 --> 00:07:42.880 align:middle line:90% in the ether. 00:07:42.880 --> 00:07:46.420 align:middle line:84% So here's where he lays out, for his new readers, what we would 00:07:46.420 --> 00:07:48.490 align:middle line:90% now call Maxwell's equations. 00:07:48.490 --> 00:07:52.840 align:middle line:84% We had a little taste of that in the excerpt for the last class. 00:07:52.840 --> 00:07:55.960 align:middle line:84% They look like this, this orange box here. 00:07:55.960 --> 00:07:58.420 align:middle line:90% They look horrifying, right? 00:07:58.420 --> 00:08:01.900 align:middle line:84% Imagine if you had to manipulate Maxwell's equations always 00:08:01.900 --> 00:08:04.300 align:middle line:90% in this full component form. 00:08:04.300 --> 00:08:07.900 align:middle line:84% As many, maybe all of you know by now, 00:08:07.900 --> 00:08:12.220 align:middle line:84% most of the central quantities in electromagnetism 00:08:12.220 --> 00:08:13.510 align:middle line:90% are vector quantities. 00:08:13.510 --> 00:08:16.280 align:middle line:84% They have both magnitude and direction. 00:08:16.280 --> 00:08:18.190 align:middle line:84% So we have to keep track of what's 00:08:18.190 --> 00:08:20.770 align:middle line:84% their component in the x direction, in the y direction, 00:08:20.770 --> 00:08:22.520 align:middle line:90% in the z direction, and so on. 00:08:22.520 --> 00:08:26.165 align:middle line:84% And so they would write those out component by component. 00:08:26.165 --> 00:08:27.790 align:middle line:84% So just writing down things like what's 00:08:27.790 --> 00:08:32.289 align:middle line:84% the energy density stored in the field would take half a page. 00:08:32.289 --> 00:08:36.130 align:middle line:84% So it's only a later Maxwellian, in this case 00:08:36.130 --> 00:08:40.360 align:middle line:84% Oliver Heaviside, who actually invented vector notation 00:08:40.360 --> 00:08:43.780 align:middle line:84% precisely to make it easier to handle Maxwell's work. 00:08:43.780 --> 00:08:45.850 align:middle line:84% It wasn't to handle any old set of vectors. 00:08:45.850 --> 00:08:49.540 align:middle line:84% It was to handle Maxwell's work in this otherwise massive, 00:08:49.540 --> 00:08:52.480 align:middle line:84% back-breaking, 900-page treatise. 00:08:52.480 --> 00:08:55.420 align:middle line:84% So nowadays, at the height of fashion, 00:08:55.420 --> 00:08:57.460 align:middle line:84% we can each proudly wear a t-shirt 00:08:57.460 --> 00:09:00.580 align:middle line:84% that has all of Maxwell's equations, only four lines, 00:09:00.580 --> 00:09:04.210 align:middle line:84% because we can use Heaviside's really quite efficient vector 00:09:04.210 --> 00:09:07.420 align:middle line:84% notation both to represent vector quantities, 00:09:07.420 --> 00:09:09.730 align:middle line:84% like the electric field and the magnetic field, 00:09:09.730 --> 00:09:12.730 align:middle line:84% but also these differential operators, like the divergence, 00:09:12.730 --> 00:09:14.470 align:middle line:84% the gradient, the curl, and so on. 00:09:14.470 --> 00:09:17.600 align:middle line:84% These were literally invented to handle Maxwell's equations, 00:09:17.600 --> 00:09:19.930 align:middle line:84% so we wouldn't all have to do this horribleness 00:09:19.930 --> 00:09:21.290 align:middle line:90% for the rest of our lives. 00:09:21.290 --> 00:09:24.890 align:middle line:84% So if you proudly have a t-shirt with Maxwell's equations, 00:09:24.890 --> 00:09:26.500 align:middle line:84% you should thank Oliver Heaviside. 00:09:26.500 --> 00:09:30.620 align:middle line:84% It fits on one t-shirt because of his innovations. 00:09:30.620 --> 00:09:32.470 align:middle line:84% Now, what's really fascinating to me, 00:09:32.470 --> 00:09:34.845 align:middle line:84% what I want to spend a little time on for this first part 00:09:34.845 --> 00:09:36.970 align:middle line:84% of the lecture, is not just that we now 00:09:36.970 --> 00:09:40.450 align:middle line:84% have a more efficient notation to handle vectors, 00:09:40.450 --> 00:09:43.060 align:middle line:84% but that what Maxwell's equations seem 00:09:43.060 --> 00:09:46.570 align:middle line:84% to mean to Maxwell and his immediate peers is really 00:09:46.570 --> 00:09:48.400 align:middle line:84% quite different from what we take 00:09:48.400 --> 00:09:50.140 align:middle line:90% those same equations to mean. 00:09:50.140 --> 00:09:52.570 align:middle line:84% So for today's class, you had a reading, 00:09:52.570 --> 00:09:57.250 align:middle line:84% a portion of an article to read by the historian Jed Buchwald. 00:09:57.250 --> 00:09:59.290 align:middle line:84% That article was later incorporated 00:09:59.290 --> 00:10:02.050 align:middle line:84% into this really interesting book called From Maxwell 00:10:02.050 --> 00:10:02.800 align:middle line:90% to Microphysics. 00:10:02.800 --> 00:10:05.350 align:middle line:84% You see its cover shown right here. 00:10:05.350 --> 00:10:09.520 align:middle line:84% So I want to follow Jed's lead in walking 00:10:09.520 --> 00:10:11.620 align:middle line:84% through a few of these examples of just how 00:10:11.620 --> 00:10:15.310 align:middle line:84% different conceptually Maxwell and his immediate circle 00:10:15.310 --> 00:10:17.980 align:middle line:84% thought his own equations applied to the world 00:10:17.980 --> 00:10:20.440 align:middle line:84% compared to how we use those same equations. 00:10:20.440 --> 00:10:21.635 align:middle line:90% We still buy the t-shirt. 00:10:21.635 --> 00:10:23.260 align:middle line:84% We think those equations mean something 00:10:23.260 --> 00:10:25.090 align:middle line:90% quite different today. 00:10:25.090 --> 00:10:28.078 align:middle line:84% I should say Jed Buchwald is a colleague of mine. 00:10:28.078 --> 00:10:29.620 align:middle line:84% He taught for many years here at MIT. 00:10:29.620 --> 00:10:31.700 align:middle line:90% He's now a professor at Caltech. 00:10:31.700 --> 00:10:35.120 align:middle line:84% But this is stuff that I think is really just amazing. 00:10:35.120 --> 00:10:35.620 align:middle line:90% OK. 00:10:35.620 --> 00:10:38.110 align:middle line:84% So to us, Maxwell's equations describe 00:10:38.110 --> 00:10:41.270 align:middle line:84% the behavior of fundamental or elementary 00:10:41.270 --> 00:10:44.270 align:middle line:84% charged particles, things like electrons, or ions, 00:10:44.270 --> 00:10:46.760 align:middle line:84% or even protons, and quarks, and things we'll 00:10:46.760 --> 00:10:48.180 align:middle line:90% get to later in this term. 00:10:48.180 --> 00:10:50.000 align:middle line:84% So to us, Maxwell's equations talking 00:10:50.000 --> 00:10:53.000 align:middle line:84% about objects that have a fixed amount of electric charge 00:10:53.000 --> 00:10:55.760 align:middle line:84% that's stapled onto them, doesn't change. 00:10:55.760 --> 00:10:58.160 align:middle line:84% Total electric charge is conserved. 00:10:58.160 --> 00:11:00.380 align:middle line:84% You can't change the overall amount 00:11:00.380 --> 00:11:04.040 align:middle line:84% of, say, plus or minus charge in the universe. 00:11:04.040 --> 00:11:07.970 align:middle line:84% You have a fixed amount of electric charge attached, 00:11:07.970 --> 00:11:11.510 align:middle line:84% a constant amount attached to each microscopic charge 00:11:11.510 --> 00:11:12.920 align:middle line:90% carrier, like an electron. 00:11:12.920 --> 00:11:15.830 align:middle line:84% We would say the charge on an electron is 1 unit. 00:11:15.830 --> 00:11:18.980 align:middle line:84% It doesn't later become 1.3 units on one electron. 00:11:18.980 --> 00:11:22.970 align:middle line:84% It's a fixed amount per fundamental charge. 00:11:22.970 --> 00:11:25.910 align:middle line:84% And then electrical phenomena, like electric current, 00:11:25.910 --> 00:11:28.850 align:middle line:84% is nothing other than those little fundamental charge 00:11:28.850 --> 00:11:30.440 align:middle line:90% carriers moving around. 00:11:30.440 --> 00:11:32.510 align:middle line:84% So electric current, to us, is nothing 00:11:32.510 --> 00:11:35.390 align:middle line:84% but the motion of those elementary charge carriers 00:11:35.390 --> 00:11:36.840 align:middle line:90% or fundamental charge carriers. 00:11:36.840 --> 00:11:39.500 align:middle line:84% So we have very simple cartoons like this 00:11:39.500 --> 00:11:43.410 align:middle line:84% to make sense of things like charge and current. 00:11:43.410 --> 00:11:46.920 align:middle line:84% To Maxwell and even to most of his followers for generations, 00:11:46.920 --> 00:11:49.047 align:middle line:90% not one part of that was true. 00:11:49.047 --> 00:11:50.380 align:middle line:90% I just want to let that sink in. 00:11:50.380 --> 00:11:51.750 align:middle line:90% We use his equations. 00:11:51.750 --> 00:11:52.950 align:middle line:90% We put them on our t-shirts. 00:11:52.950 --> 00:11:54.000 align:middle line:90% We wear them proudly. 00:11:54.000 --> 00:11:55.410 align:middle line:90% I wear them proudly. 00:11:55.410 --> 00:11:57.780 align:middle line:84% And yet, what we think those literally 00:11:57.780 --> 00:12:01.500 align:middle line:84% exact same equations refer to is almost 100% 00:12:01.500 --> 00:12:04.620 align:middle line:84% reversed from how Maxwell himself thought about them 00:12:04.620 --> 00:12:06.810 align:middle line:84% or how his peers and students did. 00:12:06.810 --> 00:12:08.680 align:middle line:84% And if you pause for a moment, you say, 00:12:08.680 --> 00:12:10.460 align:middle line:90% well, it had to be that way. 00:12:10.460 --> 00:12:12.960 align:middle line:84% Some of you may know-- and we'll look at this in a few weeks 00:12:12.960 --> 00:12:14.760 align:middle line:90% if this is news to you-- 00:12:14.760 --> 00:12:16.890 align:middle line:84% the electron itself wasn't discovered-- 00:12:16.890 --> 00:12:18.900 align:middle line:84% or the experimental evidence that 00:12:18.900 --> 00:12:21.540 align:middle line:84% would come to be called the electron 00:12:21.540 --> 00:12:23.790 align:middle line:84% didn't even coalesce for about 20 years 00:12:23.790 --> 00:12:26.310 align:middle line:84% after Maxwell had published his treatise. 00:12:26.310 --> 00:12:29.310 align:middle line:84% He writes these 900 pages in 1873. 00:12:29.310 --> 00:12:32.460 align:middle line:84% It's only in the early and mid-1890s, 00:12:32.460 --> 00:12:34.740 align:middle line:84% two decades later, that physicists 00:12:34.740 --> 00:12:36.930 align:middle line:84% start to have any kind of empirical evidence 00:12:36.930 --> 00:12:39.700 align:middle line:84% that something like an electron is part of the world. 00:12:39.700 --> 00:12:42.000 align:middle line:84% So the Maxwellians were not thinking 00:12:42.000 --> 00:12:45.700 align:middle line:84% about fundamental or elementary charges that zip around 00:12:45.700 --> 00:12:47.590 align:middle line:90% with fixed charge per particle. 00:12:47.590 --> 00:12:49.690 align:middle line:84% They were thinking about a continuum, 00:12:49.690 --> 00:12:53.980 align:middle line:84% as we've seen many times now, this elastic continuous medium 00:12:53.980 --> 00:12:56.170 align:middle line:90% of the light-bearing ether. 00:12:56.170 --> 00:13:00.610 align:middle line:84% So Jed Buchwald calls the Maxwellians inverted atomists. 00:13:00.610 --> 00:13:02.770 align:middle line:84% So I think that's a pretty helpful term. 00:13:02.770 --> 00:13:05.230 align:middle line:84% They believed in things like chemical atoms. 00:13:05.230 --> 00:13:06.700 align:middle line:84% But they didn't believe that there 00:13:06.700 --> 00:13:11.090 align:middle line:84% were fundamental constituents that had unchanging properties. 00:13:11.090 --> 00:13:13.060 align:middle line:84% So as Jed nicely puts it, instead 00:13:13.060 --> 00:13:16.450 align:middle line:84% of building the world out of atoms the way we would imagine, 00:13:16.450 --> 00:13:19.120 align:middle line:84% the Maxwellians built atoms out of the world. 00:13:19.120 --> 00:13:20.590 align:middle line:84% And by the world, he really means 00:13:20.590 --> 00:13:23.920 align:middle line:84% this continuum, elastic medium of the ether. 00:13:23.920 --> 00:13:26.800 align:middle line:84% So things like atoms or charges were 00:13:26.800 --> 00:13:30.915 align:middle line:84% coagulations of this more primary stuff, the ether. 00:13:30.915 --> 00:13:32.290 align:middle line:84% And that has implications for how 00:13:32.290 --> 00:13:34.330 align:middle line:84% they make sense of other electric and magnetic 00:13:34.330 --> 00:13:35.017 align:middle line:90% phenomena. 00:13:35.017 --> 00:13:37.600 align:middle line:84% So here's an example I want to just take a few moments to walk 00:13:37.600 --> 00:13:40.200 align:middle line:84% through that Jed talks about in that article, 00:13:40.200 --> 00:13:42.370 align:middle line:84% in fact in that first few pages of the article 00:13:42.370 --> 00:13:44.550 align:middle line:84% that I'd assigned for today's reading. 00:13:44.550 --> 00:13:45.750 align:middle line:90% It's pretty abstract. 00:13:45.750 --> 00:13:48.360 align:middle line:84% So I hope a few pictures might help a little bit. 00:13:48.360 --> 00:13:51.585 align:middle line:84% And this is really just to give a flavor of how the Maxwellians 00:13:51.585 --> 00:13:52.710 align:middle line:90% made sense of these things. 00:13:52.710 --> 00:13:57.300 align:middle line:84% If every step of this discussion is hard to follow, that's OK. 00:13:57.300 --> 00:14:00.030 align:middle line:84% I just want to get across what they thought they were doing. 00:14:00.030 --> 00:14:02.700 align:middle line:84% It's more like how did they conceptualize 00:14:02.700 --> 00:14:05.890 align:middle line:90% things like charge and current. 00:14:05.890 --> 00:14:09.090 align:middle line:84% So to the Maxwellians, charge could drift in and out 00:14:09.090 --> 00:14:12.240 align:middle line:84% of existence because it wasn't a fundamental property attached 00:14:12.240 --> 00:14:14.260 align:middle line:90% to fundamental particles. 00:14:14.260 --> 00:14:17.460 align:middle line:84% Instead, it was a kind of reflection of the underlying 00:14:17.460 --> 00:14:18.810 align:middle line:90% state of the ether. 00:14:18.810 --> 00:14:23.130 align:middle line:84% It was a local manifestation of these stresses or strains 00:14:23.130 --> 00:14:24.120 align:middle line:90% in the ether. 00:14:24.120 --> 00:14:27.870 align:middle line:84% So to take one example, charge could arise, for example, 00:14:27.870 --> 00:14:29.700 align:middle line:84% as a surface effect-- not only this way, 00:14:29.700 --> 00:14:31.410 align:middle line:84% but this is one example and one that I 00:14:31.410 --> 00:14:33.240 align:middle line:84% think Jed treats pretty nicely, pretty 00:14:33.240 --> 00:14:34.900 align:middle line:90% helpfully in that article. 00:14:34.900 --> 00:14:38.370 align:middle line:84% So one way you might encounter electric charge building up, 00:14:38.370 --> 00:14:40.500 align:middle line:84% according to the Maxwellians, was 00:14:40.500 --> 00:14:43.200 align:middle line:84% if you had a change in two different kinds of materials 00:14:43.200 --> 00:14:44.740 align:middle line:90% near each other in space. 00:14:44.740 --> 00:14:46.820 align:middle line:84% It would be a kind of surface or boundary effect. 00:14:46.820 --> 00:14:49.430 align:middle line:84% Let's talk about what they meant by that. 00:14:49.430 --> 00:14:51.280 align:middle line:84% Imagine you had these two conducting 00:14:51.280 --> 00:14:54.400 align:middle line:84% plates, these thick black lines on either side. 00:14:54.400 --> 00:14:59.170 align:middle line:84% And you put a voltage difference across them. 00:14:59.170 --> 00:15:01.900 align:middle line:84% You charge one up with a positive voltage and the other 00:15:01.900 --> 00:15:02.750 align:middle line:90% with a negative. 00:15:02.750 --> 00:15:05.590 align:middle line:84% So between them, you'd have some net voltage 00:15:05.590 --> 00:15:08.440 align:middle line:84% change between the two conducting plates. 00:15:08.440 --> 00:15:10.620 align:middle line:84% So according to Maxwell and his circle, 00:15:10.620 --> 00:15:12.370 align:middle line:84% that meant that what you were really doing 00:15:12.370 --> 00:15:15.040 align:middle line:84% is putting this elastic ether under tension. 00:15:15.040 --> 00:15:18.550 align:middle line:84% The ether that would be in the space between those two plates 00:15:18.550 --> 00:15:22.420 align:middle line:84% would now be not at some resting or equilibrium state. 00:15:22.420 --> 00:15:24.580 align:middle line:84% You've put it under strain or tension. 00:15:24.580 --> 00:15:27.820 align:middle line:84% In fact, fun fact, I believe it's the case to this day 00:15:27.820 --> 00:15:31.360 align:middle line:84% that the French word for voltage is actually tension, 00:15:31.360 --> 00:15:32.530 align:middle line:90% like tension. 00:15:32.530 --> 00:15:34.060 align:middle line:84% So it really was a notion that you 00:15:34.060 --> 00:15:36.130 align:middle line:84% were putting the physical medium under tension 00:15:36.130 --> 00:15:38.930 align:middle line:84% when you apply this voltage, this voltage difference. 00:15:38.930 --> 00:15:41.540 align:middle line:84% So now, the potential energy stored in the ether-- 00:15:41.540 --> 00:15:45.160 align:middle line:84% I think about squeezing a spring, that mechanical ether. 00:15:45.160 --> 00:15:47.800 align:middle line:84% The rate at which that energy would be dissipated, 00:15:47.800 --> 00:15:51.670 align:middle line:84% would be relaxed, is controlled by the intervening stuff. 00:15:51.670 --> 00:15:54.430 align:middle line:84% So in this case, they imagined they had two different kinds 00:15:54.430 --> 00:15:58.240 align:middle line:84% of material filling this space between the two conducting 00:15:58.240 --> 00:16:00.670 align:middle line:84% plates that we'll just call the blue region 00:16:00.670 --> 00:16:01.928 align:middle line:90% and the green region. 00:16:01.928 --> 00:16:03.970 align:middle line:84% And because they're different kinds of materials, 00:16:03.970 --> 00:16:06.160 align:middle line:84% they have different physical properties. 00:16:06.160 --> 00:16:08.710 align:middle line:84% In particular, they could store up 00:16:08.710 --> 00:16:12.502 align:middle line:84% and/or dissipate this local strain at different rates. 00:16:12.502 --> 00:16:13.960 align:middle line:84% This is, again, how the Maxwellians 00:16:13.960 --> 00:16:15.200 align:middle line:90% would have talked about it. 00:16:15.200 --> 00:16:17.020 align:middle line:84% So in the blue medium, they would 00:16:17.020 --> 00:16:20.320 align:middle line:84% have one characteristic elastic capacity. 00:16:20.320 --> 00:16:22.750 align:middle line:84% It's what we would call the dielectric constant. 00:16:22.750 --> 00:16:25.240 align:middle line:84% We would still use the same Greek letter, epsilon. 00:16:25.240 --> 00:16:28.720 align:middle line:84% To them, it really was like a spring constant. 00:16:28.720 --> 00:16:30.850 align:middle line:84% How do you store up potential energy 00:16:30.850 --> 00:16:34.420 align:middle line:84% by putting that medium under a strain, like squeezing a spring 00:16:34.420 --> 00:16:36.220 align:middle line:90% or stretching a spring? 00:16:36.220 --> 00:16:39.490 align:middle line:84% So on the one hand, you have a how easy can you 00:16:39.490 --> 00:16:41.050 align:middle line:90% store the potential energy. 00:16:41.050 --> 00:16:43.560 align:middle line:84% And the other relevant constant, or 00:16:43.560 --> 00:16:45.600 align:middle line:84% characteristic of that material, they 00:16:45.600 --> 00:16:47.250 align:middle line:90% called the conducting capacity. 00:16:47.250 --> 00:16:49.150 align:middle line:84% We simply call it the conductivity. 00:16:49.150 --> 00:16:51.730 align:middle line:84% And we use, again, the same Greek letter, sigma. 00:16:51.730 --> 00:16:55.050 align:middle line:84% And the point was, in these two different kinds of materials, 00:16:55.050 --> 00:16:57.430 align:middle line:84% they would have different properties. 00:16:57.430 --> 00:17:00.990 align:middle line:84% So the blue material has one characteristic elastic 00:17:00.990 --> 00:17:03.540 align:middle line:84% capacity, some other quantitative value 00:17:03.540 --> 00:17:07.829 align:middle line:84% for its conducting capacity-- epsilon 1 and sigma 1. 00:17:07.829 --> 00:17:10.410 align:middle line:84% And this green region, made of some other kind of stuff, 00:17:10.410 --> 00:17:13.050 align:middle line:84% would have different values for those two basically 00:17:13.050 --> 00:17:14.410 align:middle line:90% like spring constants. 00:17:14.410 --> 00:17:17.550 align:middle line:84% So the rate at which the tension, the underlying tension 00:17:17.550 --> 00:17:19.380 align:middle line:84% of the ether, could be dissipated 00:17:19.380 --> 00:17:21.750 align:middle line:84% was a kind of competition between those effects. 00:17:21.750 --> 00:17:24.089 align:middle line:84% You store up tension and you dissipate it 00:17:24.089 --> 00:17:27.359 align:middle line:84% at different rates, given by, let's say, the ratio tau 00:17:27.359 --> 00:17:32.500 align:middle line:84% of that elastic capacity divided by its conducting capacity. 00:17:32.500 --> 00:17:34.890 align:middle line:84% So then what happens at the boundaries-- now, 00:17:34.890 --> 00:17:37.990 align:middle line:84% you have different rates of dissipating this underlying 00:17:37.990 --> 00:17:38.490 align:middle line:90% tension. 00:17:38.490 --> 00:17:42.000 align:middle line:84% So you can build up a surface charge as a boundary effect, 00:17:42.000 --> 00:17:43.270 align:middle line:90% as a surface effect. 00:17:43.270 --> 00:17:46.660 align:middle line:84% So sure, electric charge could be very important. 00:17:46.660 --> 00:17:48.545 align:middle line:90% But it wasn't like vital. 00:17:48.545 --> 00:17:49.920 align:middle line:84% To the Maxwellians, it was a kind 00:17:49.920 --> 00:17:53.370 align:middle line:84% of accidental effect of the real physics, which 00:17:53.370 --> 00:17:55.950 align:middle line:84% you have on the elastic medium of the ether. 00:17:55.950 --> 00:18:00.390 align:middle line:84% And it can locally discharge or dissipate that tension 00:18:00.390 --> 00:18:02.820 align:middle line:84% at different rates given the material properties 00:18:02.820 --> 00:18:05.220 align:middle line:84% of the stuff that fills the region-- 00:18:05.220 --> 00:18:06.810 align:middle line:84% the blue region or the green region. 00:18:06.810 --> 00:18:09.750 align:middle line:84% So the surface charge was not very important. 00:18:09.750 --> 00:18:11.130 align:middle line:90% It was ephemeral. 00:18:11.130 --> 00:18:13.050 align:middle line:84% At some function of time, it's going 00:18:13.050 --> 00:18:15.330 align:middle line:84% to float into or out of existence. 00:18:15.330 --> 00:18:18.090 align:middle line:84% And it really comes from more fundamental processes 00:18:18.090 --> 00:18:19.020 align:middle line:90% involving the ether. 00:18:19.020 --> 00:18:21.480 align:middle line:84% That's how they would have characterized it. 00:18:21.480 --> 00:18:25.200 align:middle line:84% So let me just say that we can see some similarities. 00:18:25.200 --> 00:18:26.800 align:middle line:84% Perhaps the most important similarity 00:18:26.800 --> 00:18:30.720 align:middle line:84% is that for all using field theory, them and us. 00:18:30.720 --> 00:18:34.110 align:middle line:84% And we're using it, though the status of those fields 00:18:34.110 --> 00:18:35.320 align:middle line:90% is not quite the same. 00:18:35.320 --> 00:18:37.890 align:middle line:84% So it's not that quantum field theory is nothing 00:18:37.890 --> 00:18:39.320 align:middle line:90% other than a Maxwellian ether. 00:18:39.320 --> 00:18:40.650 align:middle line:90% It's certainly not that. 00:18:40.650 --> 00:18:44.580 align:middle line:84% But the notion that there's a way of characterizing 00:18:44.580 --> 00:18:47.160 align:middle line:84% how things are spread out through space 00:18:47.160 --> 00:18:49.740 align:middle line:84% and changing over time, the basic field notion, 00:18:49.740 --> 00:18:52.290 align:middle line:84% that is quite common to how we organize our thoughts today, 00:18:52.290 --> 00:18:54.470 align:middle line:84% except that-- with the difference being, 00:18:54.470 --> 00:18:56.220 align:middle line:84% even in our modern view-- and again, we'll 00:18:56.220 --> 00:18:58.830 align:middle line:84% have chance to look at this in more detail in several weeks-- 00:18:58.830 --> 00:19:00.690 align:middle line:84% in our modern view the amount of, say, 00:19:00.690 --> 00:19:05.400 align:middle line:84% electric charge is fixed per particle associated 00:19:05.400 --> 00:19:06.550 align:middle line:90% with that field. 00:19:06.550 --> 00:19:08.640 align:middle line:84% So we would say, there is a quantum field 00:19:08.640 --> 00:19:10.390 align:middle line:90% associated with the electron. 00:19:10.390 --> 00:19:11.820 align:middle line:90% And again, we'll come to this. 00:19:11.820 --> 00:19:13.290 align:middle line:90% If this is news, that's OK. 00:19:13.290 --> 00:19:15.180 align:middle line:84% We'll have time to look at it more carefully. 00:19:15.180 --> 00:19:16.950 align:middle line:84% There's a field spread out through space 00:19:16.950 --> 00:19:18.158 align:middle line:90% associated with the electron. 00:19:18.158 --> 00:19:20.610 align:middle line:84% But the individual particles, the electrons themselves, 00:19:20.610 --> 00:19:22.560 align:middle line:84% have a fixed and unchanging amount 00:19:22.560 --> 00:19:24.973 align:middle line:84% of charge nailed onto them, attached to them 00:19:24.973 --> 00:19:26.640 align:middle line:84% as part of their fundamental properties. 00:19:26.640 --> 00:19:29.790 align:middle line:84% That part had no analogy for the Maxwellians. 00:19:29.790 --> 00:19:31.440 align:middle line:90% And I find that amazing. 00:19:31.440 --> 00:19:32.830 align:middle line:90% I find that really fascinating. 00:19:32.830 --> 00:19:34.200 align:middle line:90% So it's an excellent question. 00:19:34.200 --> 00:19:35.620 align:middle line:84% I'd be glad to chat more about it. 00:19:35.620 --> 00:19:37.050 align:middle line:84% But for now, let me pause and say 00:19:37.050 --> 00:19:39.450 align:middle line:84% some similarities and sense of a field physics, 00:19:39.450 --> 00:19:41.970 align:middle line:84% but this notion of fundamental charge carriers, 00:19:41.970 --> 00:19:45.698 align:middle line:84% that's actually a pretty important disanalogy. 00:19:45.698 --> 00:19:48.240 align:middle line:84% And so in fact, that's part of what the slide is saying here, 00:19:48.240 --> 00:19:51.890 align:middle line:84% this updated slide, that we would describe these properties 00:19:51.890 --> 00:19:53.870 align:middle line:84% of these materials, like the blue material 00:19:53.870 --> 00:19:55.670 align:middle line:84% and the green material, that they're 00:19:55.670 --> 00:19:57.800 align:middle line:84% made up of fundamental objects like electrons, 00:19:57.800 --> 00:20:00.290 align:middle line:84% and protons, or even quarks, and so on 00:20:00.290 --> 00:20:02.750 align:middle line:84% that we could move around or rearrange 00:20:02.750 --> 00:20:04.850 align:middle line:84% those fundamental charge carriers. 00:20:04.850 --> 00:20:06.890 align:middle line:84% But we can't change the amount of charge 00:20:06.890 --> 00:20:08.510 align:middle line:90% per elementary particle. 00:20:08.510 --> 00:20:09.930 align:middle line:90% We can change their arrangement. 00:20:09.930 --> 00:20:11.750 align:middle line:84% And we often call that polarizing them, 00:20:11.750 --> 00:20:15.320 align:middle line:84% changing their orientation with respect to each other. 00:20:15.320 --> 00:20:18.680 align:middle line:84% We can move around those fundamental charges. 00:20:18.680 --> 00:20:22.100 align:middle line:84% And these parameters, like epsilon and sigma 00:20:22.100 --> 00:20:24.650 align:middle line:84% that the Maxwellians considered like basic spring constants, 00:20:24.650 --> 00:20:28.370 align:middle line:84% to us, those are measures of how readily we can rearrange 00:20:28.370 --> 00:20:29.660 align:middle line:90% the fundamental charges. 00:20:29.660 --> 00:20:32.390 align:middle line:84% So they're characteristics of a material, 00:20:32.390 --> 00:20:36.200 align:middle line:84% but not a characteristic of the stresses in the underlying 00:20:36.200 --> 00:20:37.070 align:middle line:90% ether. 00:20:37.070 --> 00:20:40.130 align:middle line:84% So for us, charge comes first-- elementary, 00:20:40.130 --> 00:20:43.130 align:middle line:84% unchanging, charge which is fixed to a particle. 00:20:43.130 --> 00:20:45.780 align:middle line:84% It never winks out of existence and so on. 00:20:45.780 --> 00:20:49.380 align:middle line:84% For the Maxwellians, charge was a secondary effect arising 00:20:49.380 --> 00:20:52.510 align:middle line:84% from the state of the medium, even though, as I keep saying, 00:20:52.510 --> 00:20:54.180 align:middle line:90% we use Maxwell's equations. 00:20:54.180 --> 00:20:56.730 align:middle line:84% We interpret his equations sometimes 00:20:56.730 --> 00:21:00.002 align:middle line:84% in really quite radically different ways. 00:21:00.002 --> 00:21:01.710 align:middle line:84% So I'm going to wrap up the Maxwell part. 00:21:01.710 --> 00:21:04.020 align:middle line:84% And we'll pause for more questions in a moment. 00:21:04.020 --> 00:21:06.420 align:middle line:84% So as I've now emphasized a few times, 00:21:06.420 --> 00:21:08.160 align:middle line:84% we still use Maxwell's equations. 00:21:08.160 --> 00:21:11.572 align:middle line:84% We really use Oliver Heaviside's very efficient version 00:21:11.572 --> 00:21:12.530 align:middle line:90% of Maxwell's equations. 00:21:12.530 --> 00:21:14.130 align:middle line:90% So now, it fits on one t-shirt. 00:21:14.130 --> 00:21:15.810 align:middle line:84% But the way we make sense of those 00:21:15.810 --> 00:21:20.000 align:middle line:84% is really almost a turned on its head compared to how Maxwell 00:21:20.000 --> 00:21:22.380 align:middle line:84% and, indeed, even Oliver Heaviside had interpreted them. 00:21:22.380 --> 00:21:23.950 align:middle line:90% And I find that just delicious. 00:21:23.950 --> 00:21:25.020 align:middle line:90% I think that's fantastic. 00:21:25.020 --> 00:21:27.145 align:middle line:84% We're going to come to that, by the way, many times 00:21:27.145 --> 00:21:29.670 align:middle line:84% this semester-- not only Maxwell versus us, 00:21:29.670 --> 00:21:32.290 align:middle line:84% Einstein, Heisenberg, you name it. 00:21:32.290 --> 00:21:35.070 align:middle line:84% We're going to see where we use the same equations 00:21:35.070 --> 00:21:36.240 align:middle line:90% in many instances. 00:21:36.240 --> 00:21:37.890 align:middle line:84% And yet, how we make sense of them, 00:21:37.890 --> 00:21:41.350 align:middle line:84% what we think those equations tell us about the world, 00:21:41.350 --> 00:21:44.075 align:middle line:84% not fixed, and here's an early example 00:21:44.075 --> 00:21:45.950 align:middle line:84% of what's going to be actually a common trend 00:21:45.950 --> 00:21:48.380 align:middle line:90% throughout the term. 00:21:48.380 --> 00:21:50.870 align:middle line:84% Moreover, for Maxwell much like for Faraday 00:21:50.870 --> 00:21:53.100 align:middle line:84% and for William Thomson, the ether came first. 00:21:53.100 --> 00:21:54.780 align:middle line:90% We saw a lot of that last time. 00:21:54.780 --> 00:21:57.290 align:middle line:84% Here's a few more examples even today. 00:21:57.290 --> 00:21:59.720 align:middle line:84% And they develop this mechanical worldview, 00:21:59.720 --> 00:22:02.180 align:middle line:84% that this is an elastic medium that we 00:22:02.180 --> 00:22:05.330 align:middle line:84% want to analyze-- basically, again, a set of stresses, 00:22:05.330 --> 00:22:08.540 align:middle line:84% strains, spring constant-type physics 00:22:08.540 --> 00:22:12.230 align:middle line:84% about putting this elastic medium under strain. 00:22:12.230 --> 00:22:13.640 align:middle line:90% It's all about continuity. 00:22:13.640 --> 00:22:17.510 align:middle line:84% All of physics came down to the behavior of this evenly spread 00:22:17.510 --> 00:22:20.810 align:middle line:84% out elastic medium, which supports contiguous, 00:22:20.810 --> 00:22:23.173 align:middle line:84% like nearest neighbor local actions. 00:22:23.173 --> 00:22:25.340 align:middle line:84% No point particles-- remember, there's no such thing 00:22:25.340 --> 00:22:27.298 align:middle line:84% as the electron, as far as they were concerned, 00:22:27.298 --> 00:22:30.950 align:middle line:84% no fundamental charges, , all these time-varying states 00:22:30.950 --> 00:22:31.553 align:middle line:90% of the ether. 00:22:31.553 --> 00:22:32.720 align:middle line:90% So I'm going to pause there. 00:22:32.720 --> 00:22:35.752 align:middle line:84% I'll stop sharing screen, see if anyone else has any questions. 00:22:35.752 --> 00:22:37.460 align:middle line:84% That was a great question we had already. 00:22:37.460 --> 00:22:38.870 align:middle line:90% Any other thoughts on Maxwell? 00:22:38.870 --> 00:22:43.660 align:middle line:90% 00:22:43.660 --> 00:22:45.340 align:middle line:84% Oh, and I see now in the chat Jade also 00:22:45.340 --> 00:22:47.680 align:middle line:84% posted an excellent point that, even in English 00:22:47.680 --> 00:22:49.730 align:middle line:84% let alone in French, we still call-- we still 00:22:49.730 --> 00:22:50.980 align:middle line:90% talk about high tension lines. 00:22:50.980 --> 00:22:52.188 align:middle line:90% That's a great example, Jade. 00:22:52.188 --> 00:22:54.820 align:middle line:90% I agree, good example. 00:22:54.820 --> 00:22:58.270 align:middle line:84% So our course 6 majors, are electrical engineers 00:22:58.270 --> 00:23:00.220 align:middle line:84% in particular, are probably not learning 00:23:00.220 --> 00:23:01.810 align:middle line:90% how to manipulate the ether. 00:23:01.810 --> 00:23:04.270 align:middle line:84% And yet, we're still using Maxwell's equations 00:23:04.270 --> 00:23:08.110 align:middle line:84% to do things like to manage things like high tension lines. 00:23:08.110 --> 00:23:09.040 align:middle line:90% Great example. 00:23:09.040 --> 00:23:11.140 align:middle line:84% Any other questions on the Maxwell stuff? 00:23:11.140 --> 00:23:15.390 align:middle line:90% 00:23:15.390 --> 00:23:18.575 align:middle line:84% A momentary disturbance in the ether? 00:23:18.575 --> 00:23:20.950 align:middle line:84% There was a great disturbance in the force, we might say. 00:23:20.950 --> 00:23:26.430 align:middle line:84% So there was a local tension of the ether 00:23:26.430 --> 00:23:28.350 align:middle line:90% because we've acted on it. 00:23:28.350 --> 00:23:30.750 align:middle line:84% We've intervened on the ether, they would have said. 00:23:30.750 --> 00:23:33.210 align:middle line:84% Because we've set up this conducting plate, and that 00:23:33.210 --> 00:23:36.810 align:middle line:84% conducting plate, and probably some big fat chemical 00:23:36.810 --> 00:23:41.340 align:middle line:84% battery with big chunky wires, we've done stuff locally. 00:23:41.340 --> 00:23:47.462 align:middle line:84% And we haven't done stuff only to an evacuated region. 00:23:47.462 --> 00:23:49.170 align:middle line:84% We're not doing this in a region where we 00:23:49.170 --> 00:23:50.688 align:middle line:90% sucked all the other stuff out. 00:23:50.688 --> 00:23:52.230 align:middle line:84% We're doing it in a region where it's 00:23:52.230 --> 00:23:54.990 align:middle line:84% filled with one kind of maybe rubbery substance 00:23:54.990 --> 00:23:58.080 align:middle line:84% or what we now call a dielectric material, 00:23:58.080 --> 00:23:59.730 align:middle line:84% like an insulating material, let's say, 00:23:59.730 --> 00:24:01.218 align:middle line:90% and some other material. 00:24:01.218 --> 00:24:02.760 align:middle line:84% And so what happens at the boundaries 00:24:02.760 --> 00:24:04.200 align:middle line:90% between those materials? 00:24:04.200 --> 00:24:07.635 align:middle line:84% Because the ether is trying to dissipate that local tension, 00:24:07.635 --> 00:24:10.260 align:middle line:84% the ether is trying to get back to a kind of equilibrium state, 00:24:10.260 --> 00:24:14.070 align:middle line:84% you might say, and the rate at which it approaches equilibrium 00:24:14.070 --> 00:24:17.000 align:middle line:84% depends on the other stuff that's in that region, 00:24:17.000 --> 00:24:18.670 align:middle line:90% so to speak, on top of it. 00:24:18.670 --> 00:24:21.970 align:middle line:84% So how quickly it can dissipate that local disturbance, 00:24:21.970 --> 00:24:24.970 align:middle line:84% that local tension, depends on what 00:24:24.970 --> 00:24:27.160 align:middle line:84% they would have called the elastic properties 00:24:27.160 --> 00:24:27.940 align:middle line:90% of the medium. 00:24:27.940 --> 00:24:30.778 align:middle line:84% Take all the stuff that's in that region of space, 00:24:30.778 --> 00:24:33.070 align:middle line:84% the ether and any other junk we've thrown on top of it, 00:24:33.070 --> 00:24:35.290 align:middle line:84% how quickly can that tension be relaxed? 00:24:35.290 --> 00:24:38.140 align:middle line:84% And we have different rates of trying 00:24:38.140 --> 00:24:41.320 align:middle line:84% to return to a kind of equilibrium 00:24:41.320 --> 00:24:43.450 align:middle line:84% based on these local spring constants. 00:24:43.450 --> 00:24:49.090 align:middle line:90% 00:24:49.090 --> 00:24:50.173 align:middle line:90% I think that's right. 00:24:50.173 --> 00:24:51.590 align:middle line:84% To be honest, it gets complicated, 00:24:51.590 --> 00:24:54.490 align:middle line:84% confusing for me as well because I was trained much 00:24:54.490 --> 00:24:55.720 align:middle line:90% more like you than like them. 00:24:55.720 --> 00:24:59.100 align:middle line:84% But my best effort, led by scholars like Jed, my effort 00:24:59.100 --> 00:25:01.600 align:middle line:84% to get into their head is much more like what you described. 00:25:01.600 --> 00:25:04.690 align:middle line:84% There's a local disturbance in the state of the ether. 00:25:04.690 --> 00:25:08.860 align:middle line:84% The ether can't instantly relax to its equilibrium 00:25:08.860 --> 00:25:09.790 align:middle line:90% configuration. 00:25:09.790 --> 00:25:12.640 align:middle line:84% The rate at which it does is this interplay 00:25:12.640 --> 00:25:17.050 align:middle line:84% between how efficiently can you store up the potential energy, 00:25:17.050 --> 00:25:19.300 align:middle line:84% and then a separate constant about how quickly you can 00:25:19.300 --> 00:25:20.470 align:middle line:90% release that stored tension. 00:25:20.470 --> 00:25:21.820 align:middle line:84% And it's that interplay that can be 00:25:21.820 --> 00:25:23.530 align:middle line:84% different in different regions of space 00:25:23.530 --> 00:25:25.822 align:middle line:84% because we've filled those regions with different kinds 00:25:25.822 --> 00:25:26.660 align:middle line:90% of materials. 00:25:26.660 --> 00:25:27.910 align:middle line:90% Those are excellent questions. 00:25:27.910 --> 00:25:30.560 align:middle line:90% 00:25:30.560 --> 00:25:31.330 align:middle line:90% OK. 00:25:31.330 --> 00:25:32.368 align:middle line:90% Let me press on. 00:25:32.368 --> 00:25:33.535 align:middle line:90% Let's look at the next part. 00:25:33.535 --> 00:25:38.520 align:middle line:90% 00:25:38.520 --> 00:25:39.020 align:middle line:90% Right. 00:25:39.020 --> 00:25:39.812 align:middle line:90% Oh good, thank you. 00:25:39.812 --> 00:25:42.050 align:middle line:90% So again, great questions. 00:25:42.050 --> 00:25:43.820 align:middle line:84% So it was really in this time period 00:25:43.820 --> 00:25:46.910 align:middle line:84% that something like electrical engineer, as a job title, 00:25:46.910 --> 00:25:48.680 align:middle line:84% was just coming into its own, in fact 00:25:48.680 --> 00:25:52.130 align:middle line:84% really in the later part of the 19th century. 00:25:52.130 --> 00:25:54.300 align:middle line:84% Maxwell, in fact, hints at that a little bit. 00:25:54.300 --> 00:25:57.643 align:middle line:84% If you remember, the preface to his massive 00:25:57.643 --> 00:25:59.060 align:middle line:84% treatise-- we had a little excerpt 00:25:59.060 --> 00:26:02.160 align:middle line:84% of that in the reading for the previous class. 00:26:02.160 --> 00:26:06.380 align:middle line:84% So even in 1873, he called them electricians. 00:26:06.380 --> 00:26:10.790 align:middle line:84% That was the word that was often used in English in, let's say, 00:26:10.790 --> 00:26:12.350 align:middle line:90% the 1870s and '80s. 00:26:12.350 --> 00:26:16.490 align:middle line:84% By the end of the century, the term electrical engineer 00:26:16.490 --> 00:26:18.740 align:middle line:84% itself would become more common even in English. 00:26:18.740 --> 00:26:21.535 align:middle line:84% But Maxwell talks about there's a demand for electricians. 00:26:21.535 --> 00:26:22.910 align:middle line:84% He really meant what we would now 00:26:22.910 --> 00:26:26.965 align:middle line:84% call electrical engineers, by and large. 00:26:26.965 --> 00:26:29.090 align:middle line:84% There's a lot of really interesting historical work 00:26:29.090 --> 00:26:33.650 align:middle line:84% on sometimes the tensions-- not just the voltage, 00:26:33.650 --> 00:26:37.010 align:middle line:84% but the actual tensions between the academic, 00:26:37.010 --> 00:26:39.810 align:middle line:84% mathematically trained, natural philosophers, 00:26:39.810 --> 00:26:43.440 align:middle line:84% like Maxwell or Lord Kelvin and the electricians 00:26:43.440 --> 00:26:47.718 align:middle line:84% who, then as now, sometimes were in institutions of higher 00:26:47.718 --> 00:26:50.010 align:middle line:84% learning, sometimes were in private practice, sometimes 00:26:50.010 --> 00:26:53.040 align:middle line:84% were in the employment of the government. 00:26:53.040 --> 00:26:57.540 align:middle line:84% And they didn't always agree on theoretical understandings. 00:26:57.540 --> 00:26:59.978 align:middle line:84% The electricians, or the engineers, often had, 00:26:59.978 --> 00:27:02.520 align:middle line:84% as far as they were concerned-- and they were usually right-- 00:27:02.520 --> 00:27:04.710 align:middle line:84% a much better understanding of how 00:27:04.710 --> 00:27:06.720 align:middle line:90% realistic materials behaved. 00:27:06.720 --> 00:27:08.550 align:middle line:90% What will be electric breakdown? 00:27:08.550 --> 00:27:10.505 align:middle line:84% Some dielectric materials really can't 00:27:10.505 --> 00:27:11.880 align:middle line:84% be loaded up with too much charge 00:27:11.880 --> 00:27:14.340 align:middle line:90% before things go haywire. 00:27:14.340 --> 00:27:18.000 align:middle line:84% So there was actually a lot given back and forth-- 00:27:18.000 --> 00:27:20.250 align:middle line:84% some of it quite friendly and constructive, some of it 00:27:20.250 --> 00:27:21.480 align:middle line:90% a bit of a rivalry. 00:27:21.480 --> 00:27:25.000 align:middle line:84% Now, people like Maxwell and Lord Thompson in particular, 00:27:25.000 --> 00:27:27.720 align:middle line:84% some of these fancy university professor types, 00:27:27.720 --> 00:27:32.460 align:middle line:84% were actually working quite a lot on advisory boards 00:27:32.460 --> 00:27:35.190 align:middle line:84% for more practical engineering, especially around things 00:27:35.190 --> 00:27:37.403 align:middle line:84% like government-sponsored telegraphy-- 00:27:37.403 --> 00:27:38.820 align:middle line:84% not only that, but including that. 00:27:38.820 --> 00:27:41.520 align:middle line:84% The telegraph was a huge driver of this stuff 00:27:41.520 --> 00:27:43.080 align:middle line:84% because the British government really 00:27:43.080 --> 00:27:44.663 align:middle line:84% wanted to have efficient communication 00:27:44.663 --> 00:27:49.140 align:middle line:84% both with its colonies and even for worldwide commerce 00:27:49.140 --> 00:27:49.990 align:middle line:90% and so on. 00:27:49.990 --> 00:27:52.677 align:middle line:84% So the priority of telegraphy among other things, soon 00:27:52.677 --> 00:27:54.510 align:middle line:84% would be things like street lighting-- we'll 00:27:54.510 --> 00:27:57.600 align:middle line:84% look at other examples-- these practical, real world needs 00:27:57.600 --> 00:28:02.370 align:middle line:84% for real electrical engineering would often bring together 00:28:02.370 --> 00:28:04.620 align:middle line:84% practical engineers, some of whom 00:28:04.620 --> 00:28:07.380 align:middle line:84% were trained in advanced mathematics, some of whom 00:28:07.380 --> 00:28:11.070 align:middle line:84% weren't, the university natural philosophers who 00:28:11.070 --> 00:28:14.362 align:middle line:84% had this mathematical training, and everything in between. 00:28:14.362 --> 00:28:16.320 align:middle line:84% So they had opportunities to interact and learn 00:28:16.320 --> 00:28:17.040 align:middle line:90% from each other. 00:28:17.040 --> 00:28:20.743 align:middle line:84% And sometimes, then as now, the physicists would say, 00:28:20.743 --> 00:28:22.410 align:middle line:84% we understand this and you're all dopes. 00:28:22.410 --> 00:28:23.940 align:middle line:84% Some of you might have heard that even today. 00:28:23.940 --> 00:28:25.773 align:middle line:84% The engineers would say, we understand this. 00:28:25.773 --> 00:28:30.090 align:middle line:84% And you physicists are chasing ridiculous, unrealistic 00:28:30.090 --> 00:28:30.790 align:middle line:90% scenarios. 00:28:30.790 --> 00:28:33.780 align:middle line:84% That is also often said today and was said then, 00:28:33.780 --> 00:28:37.540 align:middle line:84% each of those statements often with good reason. 00:28:37.540 --> 00:28:40.170 align:middle line:84% So if people are interested, some of my friends 00:28:40.170 --> 00:28:41.420 align:middle line:90% have written a lot about this. 00:28:41.420 --> 00:28:45.140 align:middle line:84% The short answer is there was a growing body of people who 00:28:45.140 --> 00:28:47.738 align:middle line:84% were professional engineers of electrical stuff, 00:28:47.738 --> 00:28:49.280 align:middle line:84% whether they were called electricians 00:28:49.280 --> 00:28:49.940 align:middle line:90% or electric engineers. 00:28:49.940 --> 00:28:50.870 align:middle line:90% That was changing. 00:28:50.870 --> 00:28:52.875 align:middle line:84% There were reasons to incentivize 00:28:52.875 --> 00:28:55.250 align:middle line:84% getting more of those folks because the government wanted 00:28:55.250 --> 00:28:56.460 align:middle line:90% a lot of them. 00:28:56.460 --> 00:28:58.710 align:middle line:84% And there were opportunities to learn from each other, 00:28:58.710 --> 00:29:00.770 align:middle line:90% sometimes with great-- 00:29:00.770 --> 00:29:04.870 align:middle line:84% smoothly and sometimes with some real name calling. 00:29:04.870 --> 00:29:06.230 align:middle line:90% It's a good question. 00:29:06.230 --> 00:29:08.750 align:middle line:84% Any other questions on this part? 00:29:08.750 --> 00:29:09.720 align:middle line:90% Excellent questions. 00:29:09.720 --> 00:29:10.220 align:middle line:90% OK. 00:29:10.220 --> 00:29:11.900 align:middle line:84% Let's go to the next part of the lecture. 00:29:11.900 --> 00:29:13.483 align:middle line:84% I hope you'll find this next part fun. 00:29:13.483 --> 00:29:15.590 align:middle line:84% I find this fantastic, I have to say. 00:29:15.590 --> 00:29:18.440 align:middle line:90% This next part is like crazy. 00:29:18.440 --> 00:29:21.080 align:middle line:84% OK, let's talk a bit more about how 00:29:21.080 --> 00:29:24.650 align:middle line:84% people like Maxwell, and Thompson, and indeed 00:29:24.650 --> 00:29:27.110 align:middle line:84% the Maxwellians, how they were encountering this material. 00:29:27.110 --> 00:29:30.170 align:middle line:84% For this part, I rely on one of my favorite books ever 00:29:30.170 --> 00:29:31.370 align:middle line:90% committed to print-- 00:29:31.370 --> 00:29:32.120 align:middle line:90% I'll go on record. 00:29:32.120 --> 00:29:33.290 align:middle line:90% I love this book-- 00:29:33.290 --> 00:29:36.080 align:middle line:84% called Masters of Theory by a colleague of mine 00:29:36.080 --> 00:29:37.430 align:middle line:90% named Andy Warwick. 00:29:37.430 --> 00:29:41.390 align:middle line:84% We're going to have an excerpt from Andy's work a little later 00:29:41.390 --> 00:29:42.230 align:middle line:90% in the class. 00:29:42.230 --> 00:29:43.820 align:middle line:84% It's assigned a few weeks from now. 00:29:43.820 --> 00:29:45.290 align:middle line:84% But here's a preview of the kinds of things 00:29:45.290 --> 00:29:47.210 align:middle line:84% that Andy writes about in this really quite amazing, I 00:29:47.210 --> 00:29:48.570 align:middle line:90% think quite amazing, book. 00:29:48.570 --> 00:29:50.720 align:middle line:84% So we saw, of course, a reminder, 00:29:50.720 --> 00:29:54.800 align:middle line:84% Michael Faraday had this practical, very modest 00:29:54.800 --> 00:29:57.260 align:middle line:84% mathematical training, a little bit of geometry, 00:29:57.260 --> 00:29:58.320 align:middle line:90% but not much else. 00:29:58.320 --> 00:29:59.930 align:middle line:84% And then we saw, by the middle decades 00:29:59.930 --> 00:30:03.350 align:middle line:84% of the 19th century, a really pretty significant shift 00:30:03.350 --> 00:30:04.940 align:middle line:84% in the training of people who cared 00:30:04.940 --> 00:30:07.790 align:middle line:84% about things like the states of the ether centered 00:30:07.790 --> 00:30:09.790 align:middle line:90% at Cambridge. 00:30:09.790 --> 00:30:13.120 align:middle line:84% One of the first things that begins to happen in the 1820s-- 00:30:13.120 --> 00:30:16.180 align:middle line:84% so basically, a little bit before William Thompson 00:30:16.180 --> 00:30:19.480 align:middle line:84% shows up as an undergraduate-- is a shift to paper. 00:30:19.480 --> 00:30:20.770 align:middle line:90% I want to let that settle in. 00:30:20.770 --> 00:30:23.890 align:middle line:84% It was weird to go to college and have 00:30:23.890 --> 00:30:26.480 align:middle line:90% to take notes on paper. 00:30:26.480 --> 00:30:29.210 align:middle line:84% And that wasn't because they all had iPads, obviously, right? 00:30:29.210 --> 00:30:31.910 align:middle line:84% It was weird to use paper because until then, 00:30:31.910 --> 00:30:35.990 align:middle line:84% what you did was practiced oral disputation and not in English 00:30:35.990 --> 00:30:38.360 align:middle line:84% but, of course, obviously in Latin. 00:30:38.360 --> 00:30:42.320 align:middle line:84% What better way to prove your mastery of Euclidean geometry 00:30:42.320 --> 00:30:45.380 align:middle line:84% than to bring your own personal chalkboard, a slate, 00:30:45.380 --> 00:30:48.980 align:middle line:84% a little personal chalkboard a couple inches big with chalk, 00:30:48.980 --> 00:30:50.880 align:middle line:84% and a compass for drawing circles, 00:30:50.880 --> 00:30:53.480 align:middle line:90% and so on, and a ruler? 00:30:53.480 --> 00:30:57.200 align:middle line:84% That's what you brought with yourself to your lectures 00:30:57.200 --> 00:30:59.360 align:middle line:84% on, let's say, Euclidean geometry. 00:30:59.360 --> 00:31:01.580 align:middle line:84% And then to show your mastery of it, 00:31:01.580 --> 00:31:06.830 align:middle line:84% you would have a dispute, like a debate, orally in Latin. 00:31:06.830 --> 00:31:09.200 align:middle line:84% You would actually debate against usually an instructor 00:31:09.200 --> 00:31:11.570 align:middle line:90% or sometimes a fellow student. 00:31:11.570 --> 00:31:12.530 align:middle line:90% I miss those days. 00:31:12.530 --> 00:31:15.793 align:middle line:84% Anyway, so it was actually weird, starting in the 1820s 00:31:15.793 --> 00:31:17.210 align:middle line:84% and '30s, when they were then told 00:31:17.210 --> 00:31:19.550 align:middle line:84% to start showing up not just with their own personal 00:31:19.550 --> 00:31:21.200 align:middle line:90% chalkboard, but with paper. 00:31:21.200 --> 00:31:23.000 align:middle line:84% It was actually still relatively expensive. 00:31:23.000 --> 00:31:24.920 align:middle line:84% They would rewrite and rewrite on it. 00:31:24.920 --> 00:31:28.080 align:middle line:84% Paper eventually becomes less expensive and less 00:31:28.080 --> 00:31:32.490 align:middle line:84% of a foreign item for a college student's toolkit. 00:31:32.490 --> 00:31:36.450 align:middle line:84% So over the 1830s, '40s, '50s, Cambridge starts 00:31:36.450 --> 00:31:39.840 align:middle line:84% going through this massive transformation 00:31:39.840 --> 00:31:43.050 align:middle line:84% in how they assess their students away 00:31:43.050 --> 00:31:46.980 align:middle line:84% from oral disputations in Latin and toward written exams 00:31:46.980 --> 00:31:48.450 align:middle line:90% on paper. 00:31:48.450 --> 00:31:51.990 align:middle line:84% In fact, the entire undergraduate study 00:31:51.990 --> 00:31:53.880 align:middle line:84% for a Cambridge undergraduate would 00:31:53.880 --> 00:31:56.850 align:middle line:84% culminate in a three-day written examination 00:31:56.850 --> 00:31:58.890 align:middle line:90% called the Mathematical Tripos. 00:31:58.890 --> 00:32:02.400 align:middle line:84% And so instead of having this scene of people like a debate 00:32:02.400 --> 00:32:06.240 align:middle line:84% club about, say, geometry or any part of mathematics, 00:32:06.240 --> 00:32:07.440 align:middle line:90% it shifted to this. 00:32:07.440 --> 00:32:08.933 align:middle line:90% You sit quietly in a room. 00:32:08.933 --> 00:32:11.100 align:middle line:84% This part probably looks a little bit more familiar, 00:32:11.100 --> 00:32:14.550 align:middle line:84% like taking SATs or some of the exams today. 00:32:14.550 --> 00:32:18.000 align:middle line:84% You sit quietly in a room, working out on paper. 00:32:18.000 --> 00:32:22.680 align:middle line:84% Your written responses are then graded by the proctors. 00:32:22.680 --> 00:32:25.800 align:middle line:84% And that was how you showed your mastery or your accomplishment 00:32:25.800 --> 00:32:26.800 align:middle line:90% of the material. 00:32:26.800 --> 00:32:29.920 align:middle line:84% Now, I made it sound like that might be familiar to us. 00:32:29.920 --> 00:32:30.510 align:middle line:90% We use paper. 00:32:30.510 --> 00:32:32.745 align:middle line:84% We take written exams not infrequently. 00:32:32.745 --> 00:32:34.620 align:middle line:84% I don't want to make this sound too familiar. 00:32:34.620 --> 00:32:37.710 align:middle line:84% What happened was a remarkable pendulum swing. 00:32:37.710 --> 00:32:40.068 align:middle line:84% So by the middle of the 19th century, 00:32:40.068 --> 00:32:41.610 align:middle line:84% it's not just that Cambridge students 00:32:41.610 --> 00:32:43.050 align:middle line:90% took this exam on paper. 00:32:43.050 --> 00:32:47.160 align:middle line:84% This was literally how they graduated from college. 00:32:47.160 --> 00:32:50.292 align:middle line:84% To get your bachelor's degree in any subject 00:32:50.292 --> 00:32:51.750 align:middle line:84% that you were studying, whether you 00:32:51.750 --> 00:32:53.875 align:middle line:84% were a philosophy student, or a literature student, 00:32:53.875 --> 00:32:56.730 align:middle line:84% or history, or mathematics, or physics, 00:32:56.730 --> 00:33:00.300 align:middle line:84% you had to pass through this Mathematical Tripos exam. 00:33:00.300 --> 00:33:02.160 align:middle line:84% There wasn't a Literature Tripos exam. 00:33:02.160 --> 00:33:04.320 align:middle line:84% This was the only way to the exit door 00:33:04.320 --> 00:33:07.080 align:middle line:84% to get your degree from Cambridge University, 00:33:07.080 --> 00:33:10.560 align:middle line:84% whether you had actually studied mathematics or not. 00:33:10.560 --> 00:33:12.840 align:middle line:90% It was a three-day exam. 00:33:12.840 --> 00:33:15.330 align:middle line:84% And in fact, your score on this one 00:33:15.330 --> 00:33:17.790 align:middle line:84% test-- not all your grades along the way, your score 00:33:17.790 --> 00:33:21.030 align:middle line:84% on this three-day written exam determined basically 00:33:21.030 --> 00:33:22.328 align:middle line:90% your graduation rank. 00:33:22.328 --> 00:33:24.120 align:middle line:84% So you go to college for a couple of years. 00:33:24.120 --> 00:33:27.842 align:middle line:84% You study a whole bunch of classes. 00:33:27.842 --> 00:33:30.620 align:middle line:84% You establish your ranking among all your peers 00:33:30.620 --> 00:33:33.440 align:middle line:84% on a three-day written exam in silence 00:33:33.440 --> 00:33:35.540 align:middle line:90% taken in the Senate House. 00:33:35.540 --> 00:33:37.880 align:middle line:84% And if that's not bad enough, then they 00:33:37.880 --> 00:33:40.470 align:middle line:84% would publish the rank order in the national newspapers. 00:33:40.470 --> 00:33:43.980 align:middle line:84% So it's bad enough to have to worry about one high stakes 00:33:43.980 --> 00:33:44.480 align:middle line:90% test. 00:33:44.480 --> 00:33:46.640 align:middle line:84% It's like the definition of a high stakes test. 00:33:46.640 --> 00:33:49.520 align:middle line:84% But then everyone you ever knew and everyone your family ever 00:33:49.520 --> 00:33:51.950 align:middle line:84% knew would see just how well or, indeed, 00:33:51.950 --> 00:33:53.700 align:middle line:90% how poorly you had done. 00:33:53.700 --> 00:33:57.530 align:middle line:84% So the very top scorers were called Wranglers. 00:33:57.530 --> 00:33:59.130 align:middle line:84% And the very top of the Wranglers 00:33:59.130 --> 00:34:00.740 align:middle line:90% was called the Senior Wrangler. 00:34:00.740 --> 00:34:03.950 align:middle line:84% That would be like any of the Wranglers with high honors, 00:34:03.950 --> 00:34:07.130 align:middle line:84% let's say, something like a magna cum laude and above 00:34:07.130 --> 00:34:09.020 align:middle line:84% or something like that or maybe cum laude. 00:34:09.020 --> 00:34:11.659 align:middle line:84% But the very top scorer, like the valedictorian, 00:34:11.659 --> 00:34:13.400 align:middle line:90% was called the Senior Wrangler. 00:34:13.400 --> 00:34:15.710 align:middle line:84% And to show just how competitive this was, 00:34:15.710 --> 00:34:18.590 align:middle line:84% both William Thompson and James Clerk Maxwell 00:34:18.590 --> 00:34:20.150 align:middle line:84% were actually only Second Wranglers, 00:34:20.150 --> 00:34:21.668 align:middle line:90% which is still pretty good. 00:34:21.668 --> 00:34:23.210 align:middle line:84% They weren't even best in their class 00:34:23.210 --> 00:34:24.679 align:middle line:84% either of their graduating years. 00:34:24.679 --> 00:34:28.440 align:middle line:84% So as Andy charts in this really fascinating book, 00:34:28.440 --> 00:34:33.570 align:middle line:84% this is a massive overhaul in how Cambridge trained everyone 00:34:33.570 --> 00:34:35.489 align:middle line:90% at the undergraduate level. 00:34:35.489 --> 00:34:37.860 align:middle line:84% Everyone passed through this Mathematical Tripos. 00:34:37.860 --> 00:34:39.630 align:middle line:90% Now, how would you do that? 00:34:39.630 --> 00:34:41.730 align:middle line:84% Very quickly, you would learn to do that 00:34:41.730 --> 00:34:46.230 align:middle line:84% not only by attending lectures, but by hiring a coach, 00:34:46.230 --> 00:34:48.360 align:middle line:90% a personal private coach. 00:34:48.360 --> 00:34:51.420 align:middle line:84% Why would they have used the word coach? 00:34:51.420 --> 00:34:54.690 align:middle line:84% Again, it puts us back in the mindset of the early and middle 00:34:54.690 --> 00:34:55.920 align:middle line:90% 19th century. 00:34:55.920 --> 00:34:58.530 align:middle line:84% One of the newest and most fascinating technologies 00:34:58.530 --> 00:35:01.860 align:middle line:84% of the day was the railroad or the railway coach. 00:35:01.860 --> 00:35:03.750 align:middle line:84% This was just coming into common usage 00:35:03.750 --> 00:35:05.257 align:middle line:84% both in Britain, and in other places 00:35:05.257 --> 00:35:07.590 align:middle line:84% throughout Europe, and the United States, and elsewhere. 00:35:07.590 --> 00:35:11.370 align:middle line:84% In the 1820s and '30s, they were called coaches, 00:35:11.370 --> 00:35:13.590 align:middle line:90% these mechanized coaches. 00:35:13.590 --> 00:35:16.020 align:middle line:84% The idea of your mathematics coach 00:35:16.020 --> 00:35:19.320 align:middle line:84% to help you get through the Mathematical Tripos exam 00:35:19.320 --> 00:35:20.880 align:middle line:84% was that, much like the railroad, 00:35:20.880 --> 00:35:24.000 align:middle line:84% the coach would literally transport you, the student, 00:35:24.000 --> 00:35:29.150 align:middle line:84% from one place to another at an unnatural, breakneck speed. 00:35:29.150 --> 00:35:31.130 align:middle line:84% So much like the railroad could go 00:35:31.130 --> 00:35:34.515 align:middle line:84% racing down the rails at speeds up to 20mph-- 00:35:34.515 --> 00:35:36.140 align:middle line:84% that wasn't very fast by our standards, 00:35:36.140 --> 00:35:39.710 align:middle line:84% but it seemed like lightning speed compared to horses. 00:35:39.710 --> 00:35:42.770 align:middle line:84% The railway coaches could transport people from one place 00:35:42.770 --> 00:35:44.450 align:middle line:84% to their destination really fast. 00:35:44.450 --> 00:35:47.990 align:middle line:84% Your mathematics coach would ferry you along 00:35:47.990 --> 00:35:50.630 align:middle line:84% at breakneck speed from your entrance of your studies 00:35:50.630 --> 00:35:53.540 align:middle line:84% toward your destination, which was the Tripos 00:35:53.540 --> 00:35:55.050 align:middle line:90% exam and your graduation. 00:35:55.050 --> 00:35:59.030 align:middle line:84% So they began calling their personal tutors coaches 00:35:59.030 --> 00:36:01.688 align:middle line:90% in recognition of the railroad. 00:36:01.688 --> 00:36:03.230 align:middle line:84% And here's one of the most successful 00:36:03.230 --> 00:36:06.050 align:middle line:84% of the later 19th century, Edward Routh, 00:36:06.050 --> 00:36:07.460 align:middle line:90% shown here with his-- 00:36:07.460 --> 00:36:09.680 align:middle line:84% I think that's Routh here, I think. 00:36:09.680 --> 00:36:10.850 align:middle line:90% They all look so similar-- 00:36:10.850 --> 00:36:15.590 align:middle line:84% with a bunch of his the pupils he was tutoring. 00:36:15.590 --> 00:36:18.290 align:middle line:84% Routh was not a professor at Cambridge. 00:36:18.290 --> 00:36:21.740 align:middle line:84% Routh was a former student who did very well on the Tripos 00:36:21.740 --> 00:36:24.890 align:middle line:84% exam, and then basically was hired out. 00:36:24.890 --> 00:36:28.020 align:middle line:84% So students would pay him directly, in addition to 00:36:28.020 --> 00:36:30.180 align:middle line:84% and separate from their university fees. 00:36:30.180 --> 00:36:32.342 align:middle line:84% They would hire a personal private tutor. 00:36:32.342 --> 00:36:34.800 align:middle line:84% And he'd set them up to work in small groups or one on one. 00:36:34.800 --> 00:36:38.220 align:middle line:84% And they would work with Routh around the clock. 00:36:38.220 --> 00:36:40.080 align:middle line:84% Now, how would you maintain that kind 00:36:40.080 --> 00:36:42.750 align:middle line:90% of discipline and schedule? 00:36:42.750 --> 00:36:46.530 align:middle line:84% By a robust program of physical exercise and exertion, 00:36:46.530 --> 00:36:49.320 align:middle line:84% like famously rowing or punting on the Cam, 00:36:49.320 --> 00:36:51.180 align:middle line:84% if any of you been to visit Cambridge. 00:36:51.180 --> 00:36:54.330 align:middle line:84% So there grows up not only a special kind of tutorial 00:36:54.330 --> 00:36:57.090 align:middle line:84% or coaching system, these coaches, 00:36:57.090 --> 00:37:00.330 align:middle line:84% but a whole associated kind of athletics program 00:37:00.330 --> 00:37:03.030 align:middle line:84% not for the joys of athletics, per se, 00:37:03.030 --> 00:37:06.120 align:middle line:84% but really to help you stay physically 00:37:06.120 --> 00:37:08.130 align:middle line:84% fit, so you can stay mentally fit, 00:37:08.130 --> 00:37:10.140 align:middle line:84% so you can spend all of your time preparing 00:37:10.140 --> 00:37:11.910 align:middle line:84% for the Mathematical Tripos exam. 00:37:11.910 --> 00:37:16.210 align:middle line:84% So then they start to call their athletic tutors coaches, right? 00:37:16.210 --> 00:37:18.510 align:middle line:84% So why do we have football coaches today? 00:37:18.510 --> 00:37:21.330 align:middle line:84% Not just because of the railway but because of the Mathematical 00:37:21.330 --> 00:37:24.405 align:middle line:90% Tripos in 19th century Britain. 00:37:24.405 --> 00:37:25.170 align:middle line:90% I love that. 00:37:25.170 --> 00:37:27.150 align:middle line:90% So the coaching was really new. 00:37:27.150 --> 00:37:30.060 align:middle line:84% And it was set up as a para-university way 00:37:30.060 --> 00:37:32.310 align:middle line:84% of shuttling these young students all 00:37:32.310 --> 00:37:35.250 align:middle line:84% the way to extraordinary mathematical skill 00:37:35.250 --> 00:37:37.240 align:middle line:90% in a short time. 00:37:37.240 --> 00:37:38.190 align:middle line:90% So here's an example. 00:37:38.190 --> 00:37:39.720 align:middle line:84% Again, I take it from Andy's book. 00:37:39.720 --> 00:37:42.690 align:middle line:84% He found some wonderful notes, and diaries, and correspondence 00:37:42.690 --> 00:37:44.550 align:middle line:84% from people who went through this system. 00:37:44.550 --> 00:37:46.050 align:middle line:84% Here's an example from someone named 00:37:46.050 --> 00:37:48.660 align:middle line:84% James Ward, who was a student preparing for the Tripos 00:37:48.660 --> 00:37:50.220 align:middle line:90% in the 1870s. 00:37:50.220 --> 00:37:52.800 align:middle line:84% This is a set of rules that he'd written out in his diary 00:37:52.800 --> 00:37:55.650 align:middle line:84% that he and his roommates had agreed to. 00:37:55.650 --> 00:37:57.360 align:middle line:84% And see which parts of this you want 00:37:57.360 --> 00:38:00.690 align:middle line:84% to take up with your roommates once for all back on campus 00:38:00.690 --> 00:38:01.682 align:middle line:90% again. 00:38:01.682 --> 00:38:03.390 align:middle line:84% The rules were-- they all agreed to this. 00:38:03.390 --> 00:38:05.550 align:middle line:84% The entire rooming block agreed to this. 00:38:05.550 --> 00:38:07.800 align:middle line:84% They would each be out of bed by 7:35. 00:38:07.800 --> 00:38:10.020 align:middle line:84% Or they could sleep in a bit more on Sundays. 00:38:10.020 --> 00:38:12.030 align:middle line:84% They would do five hours of work-- 00:38:12.030 --> 00:38:15.060 align:middle line:84% and that meant mathematics work, mathematics problem sets, 00:38:15.060 --> 00:38:16.110 align:middle line:90% before lunch. 00:38:16.110 --> 00:38:18.750 align:middle line:84% So you get up early and do five hours of math before lunch. 00:38:18.750 --> 00:38:20.040 align:middle line:90% So far, I'm interested. 00:38:20.040 --> 00:38:22.770 align:middle line:84% You do at least one hour of athletic exercise 00:38:22.770 --> 00:38:24.630 align:middle line:90% after lunch, like rowing. 00:38:24.630 --> 00:38:26.710 align:middle line:84% That's to basically help clear your mind, 00:38:26.710 --> 00:38:28.260 align:middle line:84% make sure you're ready for more math. 00:38:28.260 --> 00:38:31.470 align:middle line:84% Three hours more of math problem sets after that. 00:38:31.470 --> 00:38:33.060 align:middle line:90% Finish by 11:00 PM. 00:38:33.060 --> 00:38:35.670 align:middle line:84% Be in bed sharply by 11:30 because, the next day, 00:38:35.670 --> 00:38:36.870 align:middle line:90% you've got more math to do. 00:38:36.870 --> 00:38:39.310 align:middle line:84% And you can stay up a little bit later on Saturday. 00:38:39.310 --> 00:38:40.380 align:middle line:90% Here's the best part. 00:38:40.380 --> 00:38:43.080 align:middle line:84% You start paying in fines if you break the rules 00:38:43.080 --> 00:38:47.770 align:middle line:84% into a collective little pot of money within the rooming group. 00:38:47.770 --> 00:38:51.030 align:middle line:84% So if you break these rules, you have to start paying 3-- 00:38:51.030 --> 00:38:52.920 align:middle line:84% I remember that's 3 quid or what it is, 00:38:52.920 --> 00:38:56.130 align:middle line:84% but 3 pocket change for the first rule 00:38:56.130 --> 00:38:58.800 align:middle line:84% broken on any given day, a little bit more 00:38:58.800 --> 00:39:01.780 align:middle line:84% for every other rule broken on the same day. 00:39:01.780 --> 00:39:03.480 align:middle line:90% Now, it gets even more fun. 00:39:03.480 --> 00:39:07.800 align:middle line:84% You get paid out of that fund, that roommate kitty jar. 00:39:07.800 --> 00:39:10.140 align:middle line:84% You get paid out of that if you wake up 00:39:10.140 --> 00:39:11.340 align:middle line:90% your roommates extra early. 00:39:11.340 --> 00:39:13.530 align:middle line:84% Can you imagine your roommates being incentivized 00:39:13.530 --> 00:39:16.020 align:middle line:84% to wake you up at 6:30 instead of 7:30 00:39:16.020 --> 00:39:17.790 align:middle line:90% so you could get more math done? 00:39:17.790 --> 00:39:20.310 align:middle line:84% You'd be so grateful to them that they would get money out 00:39:20.310 --> 00:39:22.710 align:middle line:84% of this common little bit of cash. 00:39:22.710 --> 00:39:24.780 align:middle line:84% Any work that you do before 8:00 AM 00:39:24.780 --> 00:39:26.480 align:middle line:84% would count toward these other ones. 00:39:26.480 --> 00:39:29.430 align:middle line:84% So if you get up extra early and you do work even before 8:00, 00:39:29.430 --> 00:39:32.200 align:middle line:84% you can work a little bit less after lunch, for example. 00:39:32.200 --> 00:39:35.050 align:middle line:84% You get a little credit for time spent in church society 00:39:35.050 --> 00:39:35.550 align:middle line:90% meetings. 00:39:35.550 --> 00:39:36.360 align:middle line:90% I love that. 00:39:36.360 --> 00:39:38.457 align:middle line:84% And these rules are binding until further notice. 00:39:38.457 --> 00:39:39.540 align:middle line:90% I just think that's great. 00:39:39.540 --> 00:39:41.282 align:middle line:90% So these are on the slides. 00:39:41.282 --> 00:39:42.240 align:middle line:90% You can download those. 00:39:42.240 --> 00:39:44.700 align:middle line:84% If you want to set up similar rules with your roommates, 00:39:44.700 --> 00:39:47.040 align:middle line:90% I encourage you to. 00:39:47.040 --> 00:39:50.970 align:middle line:84% Now, what do you do if you take all the smart, smart, smarty 00:39:50.970 --> 00:39:53.300 align:middle line:84% pants at Cambridge University and put them 00:39:53.300 --> 00:39:55.800 align:middle line:84% through this where the only way they can graduate, no matter 00:39:55.800 --> 00:39:58.415 align:middle line:84% what subject they're actually trying to major in or study-- 00:39:58.415 --> 00:39:59.790 align:middle line:84% the only way they can graduate is 00:39:59.790 --> 00:40:02.580 align:middle line:84% by passing through this single Mathematical Tripos exam? 00:40:02.580 --> 00:40:05.580 align:middle line:84% What happens if you do that for a few generations? 00:40:05.580 --> 00:40:08.670 align:middle line:84% And I want to just let this sink in for a moment as well. 00:40:08.670 --> 00:40:10.920 align:middle line:84% What they would do on this timed exam, 00:40:10.920 --> 00:40:13.620 align:middle line:84% a three-day written exam is solved basically 00:40:13.620 --> 00:40:16.920 align:middle line:84% a lot of pretty increasingly hard math problems, 00:40:16.920 --> 00:40:19.060 align:middle line:90% math and physics problems. 00:40:19.060 --> 00:40:22.080 align:middle line:84% So an example that would be a warm-up that they would learn 00:40:22.080 --> 00:40:24.840 align:middle line:84% to do very quickly with their private coaches 00:40:24.840 --> 00:40:27.240 align:middle line:84% would be how to solve for the motion, 00:40:27.240 --> 00:40:29.930 align:middle line:84% say, of a pendulum that's swinging, 00:40:29.930 --> 00:40:31.790 align:middle line:84% if you neglect air resistance and it 00:40:31.790 --> 00:40:34.010 align:middle line:90% swings with a small amplitude. 00:40:34.010 --> 00:40:37.160 align:middle line:84% Then as now, we would recognize that the pendulum, if it 00:40:37.160 --> 00:40:39.860 align:middle line:84% has a fixed length, capital L, this 00:40:39.860 --> 00:40:41.780 align:middle line:84% is what we would call a natural frequency. 00:40:41.780 --> 00:40:44.360 align:middle line:84% What's its natural rate of swinging back and forth 00:40:44.360 --> 00:40:47.870 align:middle line:84% once we displace it from its equilibrium position 00:40:47.870 --> 00:40:50.040 align:middle line:84% and let it just gently swing back and forth? 00:40:50.040 --> 00:40:53.570 align:middle line:84% It has a frequency to execute its oscillations. 00:40:53.570 --> 00:40:56.300 align:middle line:84% And in fact, this is an example of a simple harmonic 00:40:56.300 --> 00:40:57.110 align:middle line:90% oscillator. 00:40:57.110 --> 00:40:59.170 align:middle line:84% There's a very simple equation we 00:40:59.170 --> 00:41:01.310 align:middle line:84% can write for the change of, let's say, 00:41:01.310 --> 00:41:05.090 align:middle line:84% the height of the pendulum bob above its resting position. 00:41:05.090 --> 00:41:08.870 align:middle line:84% We can characterize the height above its equilibrium spot 00:41:08.870 --> 00:41:11.570 align:middle line:90% as some amplitude phi. 00:41:11.570 --> 00:41:14.120 align:middle line:84% How will that amplitude of the height change over time? 00:41:14.120 --> 00:41:16.100 align:middle line:84% It depends on this natural frequency. 00:41:16.100 --> 00:41:18.380 align:middle line:84% And we all know on this call that we 00:41:18.380 --> 00:41:21.950 align:middle line:84% can solve this very quickly as a series of sines and cosines. 00:41:21.950 --> 00:41:26.690 align:middle line:84% It will oscillate periodically like sines and cosines. 00:41:26.690 --> 00:41:27.410 align:middle line:90% OK. 00:41:27.410 --> 00:41:31.140 align:middle line:84% What if the length of the pendulum is changing over time? 00:41:31.140 --> 00:41:33.560 align:middle line:84% So now, instead of a pendulum of fixed length, the length 00:41:33.560 --> 00:41:36.410 align:middle line:90% itself is raising and-- 00:41:36.410 --> 00:41:38.040 align:middle line:90% getting longer and shorter. 00:41:38.040 --> 00:41:40.290 align:middle line:84% So this distance changes over time. 00:41:40.290 --> 00:41:42.600 align:middle line:84% Well now, it's not actually quite so straightforward. 00:41:42.600 --> 00:41:45.320 align:middle line:84% It's no longer a simple harmonic oscillator. 00:41:45.320 --> 00:41:48.560 align:middle line:84% Let's assume that the length of the pendulum itself 00:41:48.560 --> 00:41:52.280 align:middle line:84% changes periodically, maybe with some distinct period from what 00:41:52.280 --> 00:41:55.620 align:middle line:84% would have been the average period of motion. 00:41:55.620 --> 00:41:57.830 align:middle line:84% So now, we're solving a different differential 00:41:57.830 --> 00:41:58.640 align:middle line:90% equation. 00:41:58.640 --> 00:42:01.210 align:middle line:84% If this is unfamiliar to you, good. 00:42:01.210 --> 00:42:03.710 align:middle line:84% That means you've led a healthy and productive life to date. 00:42:03.710 --> 00:42:05.930 align:middle line:84% This is the thing that the Cambridge students 00:42:05.930 --> 00:42:08.300 align:middle line:84% would learn with their private coaches 00:42:08.300 --> 00:42:11.510 align:middle line:84% because they would face these problems on a timed exam that 00:42:11.510 --> 00:42:13.340 align:middle line:84% determined their graduation honors. 00:42:13.340 --> 00:42:16.970 align:middle line:84% If you have a pendulum of periodically varying 00:42:16.970 --> 00:42:19.980 align:middle line:84% length, then the same problem to solve-- 00:42:19.980 --> 00:42:23.030 align:middle line:84% how can we characterize the height at any given moment-- 00:42:23.030 --> 00:42:25.520 align:middle line:84% that becomes not the equation for a simple harmonic 00:42:25.520 --> 00:42:28.510 align:middle line:84% oscillator, but what's called the Mathieu equation, 00:42:28.510 --> 00:42:33.030 align:middle line:84% which miraculously can be solved analytically in closed form. 00:42:33.030 --> 00:42:34.330 align:middle line:90% It's kind of amazing. 00:42:34.330 --> 00:42:37.230 align:middle line:84% But it doesn't look just like sines and cosines. 00:42:37.230 --> 00:42:40.050 align:middle line:84% And in fact, thanks to modern day computers, 00:42:40.050 --> 00:42:41.730 align:middle line:84% we can solve this pretty quickly. 00:42:41.730 --> 00:42:44.100 align:middle line:84% And it has much more complicated behavior. 00:42:44.100 --> 00:42:47.430 align:middle line:84% Instead of only a simple kind of rocking back and forth 00:42:47.430 --> 00:42:51.630 align:middle line:84% like sines and cosines, it has these periodic functions 00:42:51.630 --> 00:42:53.340 align:middle line:84% where the period is actually determined 00:42:53.340 --> 00:42:55.620 align:middle line:84% by the period at which the length is changing, 00:42:55.620 --> 00:42:57.840 align:middle line:84% and then these exponential terms-- sorry, 00:42:57.840 --> 00:43:00.720 align:middle line:84% the exponential terms which can lead either 00:43:00.720 --> 00:43:04.470 align:middle line:84% to more complicated rocking back and forth or, in fact, 00:43:04.470 --> 00:43:06.630 align:middle line:90% could lead to instabilities. 00:43:06.630 --> 00:43:08.850 align:middle line:84% You could have runaway solutions and so on, 00:43:08.850 --> 00:43:12.060 align:middle line:84% if these factors, mu, in fact are real and not only 00:43:12.060 --> 00:43:12.900 align:middle line:90% imaginary. 00:43:12.900 --> 00:43:15.240 align:middle line:84% Complicated, complicated pendulum. 00:43:15.240 --> 00:43:18.660 align:middle line:84% We don't have to solve this problem on a timed exam. 00:43:18.660 --> 00:43:21.030 align:middle line:84% I emphasize this to show this is the kind of thing 00:43:21.030 --> 00:43:23.550 align:middle line:84% you would hire a coach to help you get really good at. 00:43:23.550 --> 00:43:26.880 align:middle line:84% Starting from when you entered as an 18-year-old 00:43:26.880 --> 00:43:29.225 align:middle line:84% to when you faced this exit exam, the Tripos, 00:43:29.225 --> 00:43:30.600 align:middle line:84% you would learn to solve problems 00:43:30.600 --> 00:43:34.350 align:middle line:84% like this in closed form, and then solve 200 more of them 00:43:34.350 --> 00:43:36.430 align:middle line:90% on a timed exam over three days. 00:43:36.430 --> 00:43:38.250 align:middle line:84% And if you didn't do well, everyone 00:43:38.250 --> 00:43:39.900 align:middle line:84% would see just how poorly you did 00:43:39.900 --> 00:43:42.420 align:middle line:84% because they'd print the results in the national newspapers. 00:43:42.420 --> 00:43:44.970 align:middle line:84% Now, this came home to me rather viscerally 00:43:44.970 --> 00:43:49.140 align:middle line:84% when I was doing my own physics dissertation some years ago. 00:43:49.140 --> 00:43:51.180 align:middle line:84% To help the coaches and the students 00:43:51.180 --> 00:43:53.040 align:middle line:84% get good at this stuff, there were 00:43:53.040 --> 00:43:57.000 align:middle line:84% books written by especially successful coaches 00:43:57.000 --> 00:43:58.410 align:middle line:84% that the other coaches would use. 00:43:58.410 --> 00:43:59.520 align:middle line:90% And you just practice. 00:43:59.520 --> 00:44:02.430 align:middle line:84% It was like compendia of worked examples 00:44:02.430 --> 00:44:04.138 align:middle line:84% to help you practice like a practice exam 00:44:04.138 --> 00:44:05.597 align:middle line:84% because you'd be facing the Tripos. 00:44:05.597 --> 00:44:07.020 align:middle line:84% And you can see, they would label 00:44:07.020 --> 00:44:09.840 align:middle line:84% which Tripos this exact problem had already appeared upon. 00:44:09.840 --> 00:44:12.840 align:middle line:84% So you want to make sure you're practicing on realistic Tripos 00:44:12.840 --> 00:44:13.470 align:middle line:90% problems. 00:44:13.470 --> 00:44:15.930 align:middle line:84% This book was first published in 1902, 00:44:15.930 --> 00:44:18.720 align:middle line:84% but drawing on examples from Tripos problems 00:44:18.720 --> 00:44:19.770 align:middle line:90% throughout the 1890s. 00:44:19.770 --> 00:44:23.190 align:middle line:84% These are all, in this case, manipulating something called 00:44:23.190 --> 00:44:26.768 align:middle line:84% the Weierstrass function, the Weierstrass polynomial, which 00:44:26.768 --> 00:44:28.310 align:middle line:84% is one of the things it turns up when 00:44:28.310 --> 00:44:32.240 align:middle line:84% you start solving these complicated pendulum problems. 00:44:32.240 --> 00:44:34.410 align:middle line:84% So you want to get good at solving them fast, 00:44:34.410 --> 00:44:37.190 align:middle line:84% learn the tricks to do a coordinate transformation 00:44:37.190 --> 00:44:39.170 align:middle line:84% or see, oh, I've seen that form before. 00:44:39.170 --> 00:44:40.650 align:middle line:90% I know what to do next. 00:44:40.650 --> 00:44:42.770 align:middle line:84% Well, before I knew about the Tripos 00:44:42.770 --> 00:44:45.150 align:middle line:84% and before I knew about these coaching books, 00:44:45.150 --> 00:44:47.563 align:middle line:84% I was also trying to solve problems involving coupled 00:44:47.563 --> 00:44:49.730 align:middle line:84% oscillators that changed their fundamental frequency 00:44:49.730 --> 00:44:50.230 align:middle line:90% over time. 00:44:50.230 --> 00:44:52.370 align:middle line:84% In this case, I was studying the early universe 00:44:52.370 --> 00:44:54.680 align:middle line:90% for my PhD dissertation. 00:44:54.680 --> 00:44:58.940 align:middle line:84% And I actually reinvented or rediscovered 00:44:58.940 --> 00:45:01.790 align:middle line:84% a lot of these quite amazing analytic techniques, where 00:45:01.790 --> 00:45:04.460 align:middle line:84% you can solve for what are essentially coupled pendula, 00:45:04.460 --> 00:45:06.620 align:middle line:84% where they can change their length that determines 00:45:06.620 --> 00:45:09.620 align:middle line:84% the rate at which one elementary particle can decay 00:45:09.620 --> 00:45:10.310 align:middle line:90% into another. 00:45:10.310 --> 00:45:14.480 align:middle line:84% And it starts looking just like these coupled oscillator 00:45:14.480 --> 00:45:15.055 align:middle line:90% equations. 00:45:15.055 --> 00:45:17.180 align:middle line:84% And you solve them with things like the Weierstrass 00:45:17.180 --> 00:45:18.020 align:middle line:90% polynomials. 00:45:18.020 --> 00:45:21.943 align:middle line:84% I spent 6, or 7, or probably 8 months beating my head 00:45:21.943 --> 00:45:24.110 align:middle line:84% against this trying to solve things like the Mathieu 00:45:24.110 --> 00:45:27.210 align:middle line:84% equation and the Lame equation in closed form. 00:45:27.210 --> 00:45:29.850 align:middle line:84% It was seen as sufficiently original to warrant publication 00:45:29.850 --> 00:45:32.280 align:middle line:90% in the Physical Review in 1897. 00:45:32.280 --> 00:45:34.350 align:middle line:90% Then I met my pal, Andy Warwick. 00:45:34.350 --> 00:45:36.720 align:middle line:84% He said, oh, that was literally a homework problem 00:45:36.720 --> 00:45:39.000 align:middle line:90% for undergraduates in 1897. 00:45:39.000 --> 00:45:42.210 align:middle line:84% And so that's when it came home to me that this was basically 00:45:42.210 --> 00:45:43.380 align:middle line:90% child abuse. 00:45:43.380 --> 00:45:44.220 align:middle line:90% Let's just be clear. 00:45:44.220 --> 00:45:47.790 align:middle line:84% What Cambridge was doing was an extraordinary effort 00:45:47.790 --> 00:45:51.090 align:middle line:84% to train people in ways that look familiar to us-- 00:45:51.090 --> 00:45:54.120 align:middle line:84% timed exams, written paper problem sets-- 00:45:54.120 --> 00:45:57.180 align:middle line:84% but are actually not quite what we do either. 00:45:57.180 --> 00:46:00.690 align:middle line:84% So I learned myself the hard way-- 00:46:00.690 --> 00:46:03.120 align:middle line:84% months and months, not three days on a timed exam-- 00:46:03.120 --> 00:46:04.710 align:middle line:84% just what these undergraduates were 00:46:04.710 --> 00:46:07.690 align:middle line:84% capable of doing by the end of the 19th century. 00:46:07.690 --> 00:46:10.170 align:middle line:84% So this intense mathematical training, I want to emphasize, 00:46:10.170 --> 00:46:12.600 align:middle line:84% was not only for people who liked it. 00:46:12.600 --> 00:46:14.850 align:middle line:84% This was the only way to the exit door. 00:46:14.850 --> 00:46:17.400 align:middle line:84% Every single Cambridge student, throughout much 00:46:17.400 --> 00:46:19.530 align:middle line:84% of the 19th century, if they wanted 00:46:19.530 --> 00:46:23.190 align:middle line:84% to get their bachelor's degree in theology, in philosophy, 00:46:23.190 --> 00:46:25.720 align:middle line:84% in history, in mathematics, everyone 00:46:25.720 --> 00:46:27.430 align:middle line:84% took this Mathematical Tripos exam. 00:46:27.430 --> 00:46:30.310 align:middle line:84% Why would you ever do that to people? 00:46:30.310 --> 00:46:34.060 align:middle line:84% Again, it's an indication of the setting 00:46:34.060 --> 00:46:36.790 align:middle line:84% in which this was being done in this rapidly 00:46:36.790 --> 00:46:38.230 align:middle line:90% changing British empire. 00:46:38.230 --> 00:46:40.750 align:middle line:84% So the empire had a great need for what 00:46:40.750 --> 00:46:44.890 align:middle line:84% they considered disciplined thinkers, civil servants. 00:46:44.890 --> 00:46:47.170 align:middle line:84% And the thinking was, if you could master things 00:46:47.170 --> 00:46:50.350 align:middle line:84% like these crazy oscillator equations on a timed exam, 00:46:50.350 --> 00:46:52.420 align:middle line:84% if you could develop the mental discipline 00:46:52.420 --> 00:46:55.510 align:middle line:84% and the full-body discipline to keep yourself going 00:46:55.510 --> 00:46:58.060 align:middle line:84% for years at a time to conquer these very 00:46:58.060 --> 00:47:00.530 align:middle line:84% complicated analytic math problems, 00:47:00.530 --> 00:47:03.220 align:middle line:84% then they hoped you could conquer anything 00:47:03.220 --> 00:47:05.710 align:middle line:84% in economics, in government, in logistics, 00:47:05.710 --> 00:47:07.090 align:middle line:90% any kind of bureaucracy. 00:47:07.090 --> 00:47:10.960 align:middle line:84% This was seen as a particularly efficient way 00:47:10.960 --> 00:47:14.920 align:middle line:84% to train civil servants to handle the empire. 00:47:14.920 --> 00:47:18.280 align:middle line:84% And so as a size effect, not because this was the goal-- 00:47:18.280 --> 00:47:20.350 align:middle line:84% but as a side effect of doing this generation 00:47:20.350 --> 00:47:23.380 align:middle line:84% after generation for decades, a critical mass 00:47:23.380 --> 00:47:26.290 align:middle line:84% grew of people who went through this Tripos training 00:47:26.290 --> 00:47:28.150 align:middle line:84% and actually liked it, actually wanted 00:47:28.150 --> 00:47:30.400 align:middle line:84% to use those techniques to further 00:47:30.400 --> 00:47:32.830 align:middle line:84% their understanding of nature, like the Maxwellians, 00:47:32.830 --> 00:47:35.680 align:middle line:84% like Maxwell himself, and then indeed the generations who 00:47:35.680 --> 00:47:37.750 align:middle line:84% studied things like Maxwell's treatise. 00:47:37.750 --> 00:47:41.440 align:middle line:84% So the people who were experts in things like the divergence, 00:47:41.440 --> 00:47:44.260 align:middle line:84% and gradient, and curl, and all these great techniques 00:47:44.260 --> 00:47:47.650 align:middle line:84% for electromagnetism, they were coming out of this training 00:47:47.650 --> 00:47:50.860 align:middle line:84% not because Cambridge wanted to make more experts necessarily 00:47:50.860 --> 00:47:53.920 align:middle line:84% in mathematical physics, but because some small portion 00:47:53.920 --> 00:47:57.190 align:middle line:84% of folks who went through this increasingly common system 00:47:57.190 --> 00:47:59.110 align:middle line:84% wanted to use those skills for what we 00:47:59.110 --> 00:48:01.660 align:middle line:90% would call scientific research. 00:48:01.660 --> 00:48:04.720 align:middle line:84% And so the professionalization of this mathematically trained 00:48:04.720 --> 00:48:07.330 align:middle line:84% cohort was driven in part by demands 00:48:07.330 --> 00:48:09.850 align:middle line:84% of empire, both supplying research problems, 00:48:09.850 --> 00:48:13.390 align:middle line:84% like telegraphy or other problems in practical impact 00:48:13.390 --> 00:48:15.250 align:middle line:84% of electricity, magnetism, and optics, 00:48:15.250 --> 00:48:17.830 align:middle line:84% and also prioritizing this very specific kind 00:48:17.830 --> 00:48:19.960 align:middle line:84% of elite educational infrastructure. 00:48:19.960 --> 00:48:20.956 align:middle line:90% So let me pause there. 00:48:20.956 --> 00:48:22.331 align:middle line:84% Let's get some questions on that. 00:48:22.331 --> 00:48:25.710 align:middle line:90% 00:48:25.710 --> 00:48:26.210 align:middle line:90% Let's see. 00:48:26.210 --> 00:48:29.130 align:middle line:84% I see one of the questions was, who wrote the exams? 00:48:29.130 --> 00:48:29.630 align:middle line:90% Good. 00:48:29.630 --> 00:48:31.005 align:middle line:84% So the exams were usually written 00:48:31.005 --> 00:48:36.080 align:middle line:84% by the faculty in mathematics and physics, most of whom, 00:48:36.080 --> 00:48:39.620 align:middle line:84% at this point, had themselves gone through Cambridge. 00:48:39.620 --> 00:48:43.460 align:middle line:84% But the people writing the manuals, the help manuals, 00:48:43.460 --> 00:48:46.430 align:middle line:84% were usually recent students who had done very well. 00:48:46.430 --> 00:48:50.090 align:middle line:84% If you were a Wrangler, let alone a Senior Wrangler-- 00:48:50.090 --> 00:48:53.540 align:middle line:84% if you were in the Wrangler group, if you had high honors, 00:48:53.540 --> 00:48:55.640 align:middle line:84% then you could basically name your price. 00:48:55.640 --> 00:48:57.320 align:middle line:84% If you wanted to hang around Cambridge, 00:48:57.320 --> 00:48:59.780 align:middle line:84% you could literally make a career collecting 00:48:59.780 --> 00:49:03.580 align:middle line:84% direct student fees a dozen or so at a time and coaching 00:49:03.580 --> 00:49:05.330 align:middle line:84% these younger students through because you 00:49:05.330 --> 00:49:06.410 align:middle line:90% proved you could do it. 00:49:06.410 --> 00:49:08.460 align:middle line:84% And then you would sometimes write your own book 00:49:08.460 --> 00:49:12.060 align:middle line:84% and get royalties and sale of your training manual. 00:49:12.060 --> 00:49:16.760 align:middle line:84% So the exams themselves were the provenance of the faculty. 00:49:16.760 --> 00:49:19.430 align:middle line:84% But all the associated pedagogical materials-- 00:49:19.430 --> 00:49:21.200 align:middle line:84% the training manuals, the homework sets, 00:49:21.200 --> 00:49:23.270 align:middle line:84% and all that-- those were developed often 00:49:23.270 --> 00:49:26.010 align:middle line:90% by these private coaches. 00:49:26.010 --> 00:49:26.510 align:middle line:90% Let's see. 00:49:26.510 --> 00:49:27.802 align:middle line:90% Another meme on the way. 00:49:27.802 --> 00:49:28.760 align:middle line:90% I want to see the meme. 00:49:28.760 --> 00:49:30.920 align:middle line:84% Another question is, prior to the Tripos, 00:49:30.920 --> 00:49:32.540 align:middle line:84% had university education always been 00:49:32.540 --> 00:49:34.400 align:middle line:90% evaluated by oral disputation? 00:49:34.400 --> 00:49:37.117 align:middle line:84% By and large, or at least that was the main pattern-- 00:49:37.117 --> 00:49:39.200 align:middle line:84% not only at Cambridge, but including at Cambridge. 00:49:39.200 --> 00:49:42.375 align:middle line:84% And that goes back really to the earliest universities 00:49:42.375 --> 00:49:42.875 align:middle line:90% in Europe. 00:49:42.875 --> 00:49:44.792 align:middle line:84% There's, again, some marvelous historical work 00:49:44.792 --> 00:49:47.720 align:middle line:84% by other colleagues going back to the Middle Ages. 00:49:47.720 --> 00:49:50.180 align:middle line:84% Some of you may know Oxford was the first University 00:49:50.180 --> 00:49:51.290 align:middle line:90% in England. 00:49:51.290 --> 00:49:53.600 align:middle line:84% But that wasn't even the first in Europe, let alone 00:49:53.600 --> 00:49:55.400 align:middle line:90% other parts of the world. 00:49:55.400 --> 00:49:59.090 align:middle line:84% Oxford was founded in, roughly speaking, 1100. 00:49:59.090 --> 00:50:02.510 align:middle line:84% Cambridge was founded about a century later in around 1209. 00:50:02.510 --> 00:50:06.290 align:middle line:84% So these predate James Clerk Maxwell by centuries, 00:50:06.290 --> 00:50:08.240 align:middle line:90% by half a millennium. 00:50:08.240 --> 00:50:11.000 align:middle line:84% And for most of that time, indeed, 00:50:11.000 --> 00:50:14.240 align:middle line:84% the way of showing your command of the material 00:50:14.240 --> 00:50:16.010 align:middle line:90% was like jousting. 00:50:16.010 --> 00:50:17.625 align:middle line:90% It was oral disputes. 00:50:17.625 --> 00:50:20.000 align:middle line:84% And think about what kind of student, what kind of skills 00:50:20.000 --> 00:50:21.350 align:middle line:90% that kind of accentuates. 00:50:21.350 --> 00:50:22.937 align:middle line:90% It's kind of like-- 00:50:22.937 --> 00:50:24.770 align:middle line:84% I mean, if you speak a little disparagingly, 00:50:24.770 --> 00:50:25.980 align:middle line:90% it's like finishing school. 00:50:25.980 --> 00:50:27.690 align:middle line:90% It's like charm school, right? 00:50:27.690 --> 00:50:29.550 align:middle line:84% You want to be very quick on your feet. 00:50:29.550 --> 00:50:33.030 align:middle line:84% And you want to be persuasive in oral discussion. 00:50:33.030 --> 00:50:34.950 align:middle line:90% Those aren't bad skills to have. 00:50:34.950 --> 00:50:38.760 align:middle line:84% They're quite different skills than getting up at 6:30 00:50:38.760 --> 00:50:41.598 align:middle line:84% to do really hard math problem sets till lunch 00:50:41.598 --> 00:50:43.890 align:middle line:84% so that three years later you can solve the Mathieu you 00:50:43.890 --> 00:50:46.690 align:middle line:84% equation among 200 questions on a timed exam. 00:50:46.690 --> 00:50:49.800 align:middle line:84% So what kinds of skills are deemed most important, 00:50:49.800 --> 00:50:51.490 align:middle line:90% those aren't static. 00:50:51.490 --> 00:50:51.990 align:middle line:90% They change. 00:50:51.990 --> 00:50:52.950 align:middle line:90% They change at MIT. 00:50:52.950 --> 00:50:55.470 align:middle line:84% We go through curriculum reform, at least 00:50:55.470 --> 00:50:58.030 align:middle line:84% to some small degree, all the time. 00:50:58.030 --> 00:51:00.750 align:middle line:84% And I just find that particular transition from the oral 00:51:00.750 --> 00:51:04.872 align:middle line:84% disputations in Latin to these paper-based problem sets-- 00:51:04.872 --> 00:51:06.080 align:middle line:90% I just find that fascinating. 00:51:06.080 --> 00:51:07.538 align:middle line:84% Let's see, other questions in here. 00:51:07.538 --> 00:51:10.030 align:middle line:90% 00:51:10.030 --> 00:51:12.162 align:middle line:84% Did it affect what people chose to study? 00:51:12.162 --> 00:51:13.120 align:middle line:90% Oh, that's interesting. 00:51:13.120 --> 00:51:14.170 align:middle line:90% I'm not sure. 00:51:14.170 --> 00:51:16.480 align:middle line:84% The question is-- you can probably see in the chat-- 00:51:16.480 --> 00:51:18.190 align:middle line:84% did the Tripos exam and the esteem 00:51:18.190 --> 00:51:20.155 align:middle line:84% that came with scoring well affect 00:51:20.155 --> 00:51:21.280 align:middle line:90% what people chose to study? 00:51:21.280 --> 00:51:24.370 align:middle line:84% I don't know actually how the system had to work. 00:51:24.370 --> 00:51:28.540 align:middle line:84% I'm not sure if then, in 1850 let's say, 00:51:28.540 --> 00:51:31.270 align:middle line:84% if an undergraduate had to declare a major the way 00:51:31.270 --> 00:51:34.270 align:middle line:84% we would have to do in our modern universities. 00:51:34.270 --> 00:51:36.400 align:middle line:84% And if so, if there's information 00:51:36.400 --> 00:51:40.210 align:middle line:84% on how many students declared majors in history, or law, 00:51:40.210 --> 00:51:44.450 align:middle line:84% or medicine, or philology, and so on. 00:51:44.450 --> 00:51:47.560 align:middle line:84% So I'm not sure what the impact was on the distribution 00:51:47.560 --> 00:51:48.430 align:middle line:90% of topics studied. 00:51:48.430 --> 00:51:49.810 align:middle line:90% It's really interesting. 00:51:49.810 --> 00:51:50.650 align:middle line:90% Any would know. 00:51:50.650 --> 00:51:52.840 align:middle line:90% I should just ask Andy Warwick. 00:51:52.840 --> 00:51:56.920 align:middle line:84% What I find most striking is that even though there existed, 00:51:56.920 --> 00:51:59.470 align:middle line:84% then as now even at the time, many fields of study, 00:51:59.470 --> 00:52:03.070 align:middle line:84% or many kinds of fields to delve into more and more deeply, 00:52:03.070 --> 00:52:06.910 align:middle line:84% the only graduation requirement was the Math Tripos. 00:52:06.910 --> 00:52:08.890 align:middle line:90% I mean, that's just astonishing. 00:52:08.890 --> 00:52:10.780 align:middle line:84% Imagine if we tried that at MIT, right? 00:52:10.780 --> 00:52:14.470 align:middle line:84% I mean, sure, you can go major in political science 00:52:14.470 --> 00:52:16.780 align:middle line:90% or, heaven forbid, biology. 00:52:16.780 --> 00:52:19.480 align:middle line:84% But you have to take the Math Tripos to get out of MIT. 00:52:19.480 --> 00:52:23.210 align:middle line:90% Can you imagine the pushback? 00:52:23.210 --> 00:52:24.600 align:middle line:90% So that I find really stunning. 00:52:24.600 --> 00:52:26.390 align:middle line:84% And I think that the idea was really-- 00:52:26.390 --> 00:52:29.905 align:middle line:84% this is demonstrating a disciplined mind, 00:52:29.905 --> 00:52:31.280 align:middle line:84% according to what they considered 00:52:31.280 --> 00:52:33.620 align:middle line:84% valuable for discipline in general, 00:52:33.620 --> 00:52:36.500 align:middle line:84% but in the context of the still expanding British empire. 00:52:36.500 --> 00:52:39.140 align:middle line:90% 00:52:39.140 --> 00:52:40.290 align:middle line:90% What happened afterwards? 00:52:40.290 --> 00:52:40.790 align:middle line:90% Good. 00:52:40.790 --> 00:52:42.440 align:middle line:84% So there was beginning, in this part, 00:52:42.440 --> 00:52:45.090 align:middle line:84% in the second part of the 19th century-- 00:52:45.090 --> 00:52:47.715 align:middle line:84% there was beginning of fellowships, 00:52:47.715 --> 00:52:50.090 align:middle line:84% where if you scored-- especially if you scored very well, 00:52:50.090 --> 00:52:52.880 align:middle line:84% if you were a Senior Wrangler, really among the top Wranglers, 00:52:52.880 --> 00:52:54.290 align:middle line:90% you would then qualify-- 00:52:54.290 --> 00:52:57.950 align:middle line:84% basically get paid to get a fellowship to stay in Cambridge 00:52:57.950 --> 00:53:00.290 align:middle line:84% and not only to do so by collecting your own student 00:53:00.290 --> 00:53:01.890 align:middle line:90% fees as a coach. 00:53:01.890 --> 00:53:05.553 align:middle line:84% So it wasn't quite a tenure track position. 00:53:05.553 --> 00:53:07.470 align:middle line:84% Sometimes, if you did well on your fellowship, 00:53:07.470 --> 00:53:08.450 align:middle line:90% then you'd get hired. 00:53:08.450 --> 00:53:12.170 align:middle line:84% There was not yet a formal program of PhDs. 00:53:12.170 --> 00:53:15.350 align:middle line:84% That's really getting introduced in the very, very close 00:53:15.350 --> 00:53:16.550 align:middle line:90% of the 19th century. 00:53:16.550 --> 00:53:19.710 align:middle line:84% And that gets more common by the 1890s and forward. 00:53:19.710 --> 00:53:21.770 align:middle line:84% So there was something like a master's degree. 00:53:21.770 --> 00:53:24.380 align:middle line:84% And that, in fact, goes back quite a ways. 00:53:24.380 --> 00:53:27.170 align:middle line:84% You can get a bachelor's degree, and then get a fellowship, 00:53:27.170 --> 00:53:28.850 align:middle line:84% and then have a career at a university. 00:53:28.850 --> 00:53:31.460 align:middle line:84% Sometimes, you can get a master's, and then 00:53:31.460 --> 00:53:34.820 align:middle line:84% get hired to stay on the faculty or do other kinds of jobs. 00:53:34.820 --> 00:53:36.740 align:middle line:84% And then the more formal graduate training 00:53:36.740 --> 00:53:39.920 align:middle line:84% leading to a terminal doctoral degree, that 00:53:39.920 --> 00:53:44.060 align:middle line:84% gets built up really over the 1880s, 00:53:44.060 --> 00:53:47.977 align:middle line:90% but accelerating over the 1890s. 00:53:47.977 --> 00:53:50.060 align:middle line:84% What did pre-university maths education look like? 00:53:50.060 --> 00:53:52.190 align:middle line:90% Oh, that's a good question. 00:53:52.190 --> 00:53:53.420 align:middle line:90% It was changing slowly. 00:53:53.420 --> 00:53:55.430 align:middle line:84% Again, Andy writes about this a bit in his book. 00:53:55.430 --> 00:53:57.680 align:middle line:84% A number of the graduates of Cambridge 00:53:57.680 --> 00:54:01.380 align:middle line:84% became secondary school teachers as well as tutors and so on. 00:54:01.380 --> 00:54:04.310 align:middle line:84% So you see a dispersion effect, where people who have 00:54:04.310 --> 00:54:06.770 align:middle line:90% imbibed this program-- 00:54:06.770 --> 00:54:09.560 align:middle line:90% gotten drunk on Math Tripos-- 00:54:09.560 --> 00:54:13.220 align:middle line:84% some of them do fan out and become very influential 00:54:13.220 --> 00:54:14.300 align:middle line:90% high school teachers. 00:54:14.300 --> 00:54:17.150 align:middle line:84% And they bring an appropriate level-- 00:54:17.150 --> 00:54:19.310 align:middle line:84% they're not doing Tripos problems, per se. 00:54:19.310 --> 00:54:22.040 align:middle line:84% But they bring a more formal schooling 00:54:22.040 --> 00:54:25.395 align:middle line:84% in mathematical analysis into other parts of Britain. 00:54:25.395 --> 00:54:27.020 align:middle line:84% And it's not only happening in Britain. 00:54:27.020 --> 00:54:29.610 align:middle line:84% But there's a cool story to be told there. 00:54:29.610 --> 00:54:31.250 align:middle line:90% So it does trickle out. 00:54:31.250 --> 00:54:35.240 align:middle line:84% Not overnight, but you do see a kind of spillover effect, 00:54:35.240 --> 00:54:38.060 align:middle line:84% again, measured over, say, a few decades, 00:54:38.060 --> 00:54:41.240 align:middle line:84% not quite in William Thompson's day-- not in the 1840s, 00:54:41.240 --> 00:54:43.820 align:middle line:90% but by the 1860s, 1870s. 00:54:43.820 --> 00:54:47.630 align:middle line:84% And what happens is you can start comparing Tripos exams 00:54:47.630 --> 00:54:50.360 align:middle line:90% from the 1840s to the 1890s. 00:54:50.360 --> 00:54:52.880 align:middle line:84% You see an extraordinary acceleration 00:54:52.880 --> 00:54:55.160 align:middle line:84% of what's expected of these students in still 00:54:55.160 --> 00:54:58.293 align:middle line:84% just only three years of undergraduate training. 00:54:58.293 --> 00:55:00.710 align:middle line:84% And that's what people like Andy have looked at in detail. 00:55:00.710 --> 00:55:04.940 align:middle line:84% What becomes like a really hard Tripos problem in 1850 00:55:04.940 --> 00:55:08.030 align:middle line:84% becomes a kind of trivial one by 1880 00:55:08.030 --> 00:55:09.470 align:middle line:84% because all the kids have come in 00:55:09.470 --> 00:55:11.660 align:middle line:84% and have already trained on those. 00:55:11.660 --> 00:55:15.290 align:middle line:84% And so the acceleration of what counts as a legitimate problem 00:55:15.290 --> 00:55:16.550 align:middle line:90% is mind-boggling. 00:55:16.550 --> 00:55:20.330 align:middle line:84% And again, I love showing that comparison 00:55:20.330 --> 00:55:23.630 align:middle line:84% to Weierstrass polynomials of like undergraduates 00:55:23.630 --> 00:55:26.540 align:middle line:84% who were doing pretty well in 1890 and me 00:55:26.540 --> 00:55:30.770 align:middle line:84% struggling my tail off for months, not for hours, 00:55:30.770 --> 00:55:33.890 align:middle line:84% to reproduce what they had learned to do just 00:55:33.890 --> 00:55:34.910 align:middle line:90% to get out of college. 00:55:34.910 --> 00:55:36.380 align:middle line:84% So you can imagine, if you build up 00:55:36.380 --> 00:55:38.490 align:middle line:84% a community that's used to that, that leads 00:55:38.490 --> 00:55:39.740 align:middle line:90% to a certain kind of question. 00:55:39.740 --> 00:55:41.990 align:middle line:84% One of the things that Andy does so nicely in the book 00:55:41.990 --> 00:55:44.720 align:middle line:84% is then show that how does that then impact on how 00:55:44.720 --> 00:55:47.555 align:middle line:84% that group framed their own research questions. 00:55:47.555 --> 00:55:49.430 align:middle line:84% When they wanted to ask more about the ether, 00:55:49.430 --> 00:55:52.250 align:middle line:84% they were starting from that toolkit. 00:55:52.250 --> 00:55:53.990 align:middle line:84% And that affected, as we'll see-- 00:55:53.990 --> 00:55:55.880 align:middle line:84% a little preview-- that affected how 00:55:55.880 --> 00:55:57.350 align:middle line:84% they made sense of other new work, 00:55:57.350 --> 00:55:58.820 align:middle line:84% like Einstein's work on relativity. 00:55:58.820 --> 00:56:01.310 align:middle line:84% That's the piece that I signed from Andy for a few weeks 00:56:01.310 --> 00:56:01.980 align:middle line:90% from now. 00:56:01.980 --> 00:56:03.770 align:middle line:84% So when they encountered creative work 00:56:03.770 --> 00:56:06.260 align:middle line:84% from other scholars in other parts of the world, 00:56:06.260 --> 00:56:08.540 align:middle line:84% they would make sense of it from that toolkit. 00:56:08.540 --> 00:56:12.330 align:middle line:84% Oh, I how can I bring my tools to that cool set of questions? 00:56:12.330 --> 00:56:14.668 align:middle line:84% So it shapes what even counts as a research question. 00:56:14.668 --> 00:56:15.710 align:middle line:90% Let me move on from here. 00:56:15.710 --> 00:56:16.490 align:middle line:90% These are great questions. 00:56:16.490 --> 00:56:17.780 align:middle line:84% And I'd be glad to chat more about them. 00:56:17.780 --> 00:56:18.590 align:middle line:84% But there's a little bit more I want 00:56:18.590 --> 00:56:20.007 align:middle line:84% to get through for today's lecture 00:56:20.007 --> 00:56:22.790 align:middle line:84% because other countries-- we're going to leave Britain, 00:56:22.790 --> 00:56:24.050 align:middle line:90% at least temporarily. 00:56:24.050 --> 00:56:27.050 align:middle line:84% And let's start looking at some contrasting developments 00:56:27.050 --> 00:56:29.360 align:middle line:84% around the same time, but now on the continent. 00:56:29.360 --> 00:56:33.240 align:middle line:90% 00:56:33.240 --> 00:56:37.070 align:middle line:84% So Maxwell's work became popular not only in Britain, not only 00:56:37.070 --> 00:56:41.480 align:middle line:84% in the Cambridge circle, but pretty quickly on the continent 00:56:41.480 --> 00:56:44.990 align:middle line:84% as well, especially in the later 1880s. 00:56:44.990 --> 00:56:47.960 align:middle line:84% Remember, his treatise was published in 1873. 00:56:47.960 --> 00:56:51.140 align:middle line:84% Roughly 15 years later, it was becoming much, much 00:56:51.140 --> 00:56:53.870 align:middle line:84% more common to be taught and talked about in places 00:56:53.870 --> 00:56:55.860 align:middle line:90% like the German states-- 00:56:55.860 --> 00:56:58.980 align:middle line:84% Austria, Switzerland, and France, and so on. 00:56:58.980 --> 00:57:01.760 align:middle line:84% One of the things that helped a lot was in 1888, 15 00:57:01.760 --> 00:57:05.210 align:middle line:84% years later, a German natural researcher, Heinrich Hertz, 00:57:05.210 --> 00:57:08.030 align:middle line:84% actually succeeded in testing one of the key predictions 00:57:08.030 --> 00:57:10.820 align:middle line:84% from Maxwell's work, that these Maxwell waves, that we would 00:57:10.820 --> 00:57:13.040 align:middle line:84% now call electromagnetic radiation, 00:57:13.040 --> 00:57:16.490 align:middle line:84% could be disturbances in the ether with any kind 00:57:16.490 --> 00:57:18.290 align:middle line:84% of characteristic wavelength, not only 00:57:18.290 --> 00:57:22.110 align:middle line:84% within the visible spectrum to which our eyes are sensitive. 00:57:22.110 --> 00:57:23.990 align:middle line:84% So in modern terms, what Hertz did 00:57:23.990 --> 00:57:27.230 align:middle line:84% was generate and then detect radial waves. 00:57:27.230 --> 00:57:29.780 align:middle line:84% He was making Maxwell waves, a kind of disturbance 00:57:29.780 --> 00:57:32.610 align:middle line:84% in the ether, but with a much, much longer characteristic 00:57:32.610 --> 00:57:33.390 align:middle line:90% wavelength. 00:57:33.390 --> 00:57:36.060 align:middle line:84% And that was what Maxwell said should be possible. 00:57:36.060 --> 00:57:38.670 align:middle line:84% Hertz was among the first to demonstrate that empirically. 00:57:38.670 --> 00:57:40.320 align:middle line:84% And that really drove a lot of interest 00:57:40.320 --> 00:57:42.690 align:middle line:84% in this Maxwellian electrodynamics 00:57:42.690 --> 00:57:44.550 align:middle line:90% in the 1880s and beyond. 00:57:44.550 --> 00:57:45.972 align:middle line:84% What's really fascinating though, 00:57:45.972 --> 00:57:48.180 align:middle line:84% coming back to this theme that we've seen a few times 00:57:48.180 --> 00:57:51.540 align:middle line:84% and we'll see again, is that when these German scholars, 00:57:51.540 --> 00:57:55.260 align:middle line:84% mostly in Germany, began manipulating 00:57:55.260 --> 00:57:58.200 align:middle line:84% Maxwell's equations or their slight variations, 00:57:58.200 --> 00:58:00.450 align:middle line:84% they did so, again, by making sense of them 00:58:00.450 --> 00:58:01.260 align:middle line:90% in a different way. 00:58:01.260 --> 00:58:03.420 align:middle line:84% Even when they used the same equations, 00:58:03.420 --> 00:58:06.540 align:middle line:84% the way they interpreted them was not really always the same 00:58:06.540 --> 00:58:07.260 align:middle line:90% as Maxwell's. 00:58:07.260 --> 00:58:10.590 align:middle line:84% And here in particular, instead of following 00:58:10.590 --> 00:58:13.830 align:middle line:84% the characteristically British approach to thinking about this 00:58:13.830 --> 00:58:17.220 align:middle line:84% mechanical, elastic ether, like Lord Kelvin instructed his 00:58:17.220 --> 00:58:20.730 align:middle line:84% listeners-- stick your hand in a pot of jelly and shake it 00:58:20.730 --> 00:58:21.510 align:middle line:90% around-- 00:58:21.510 --> 00:58:23.970 align:middle line:84% instead of that, a growing number 00:58:23.970 --> 00:58:26.790 align:middle line:84% of the German electromagnetic experts 00:58:26.790 --> 00:58:28.960 align:middle line:90% began turning that on its head. 00:58:28.960 --> 00:58:30.780 align:middle line:84% They would use Maxwell's equations, 00:58:30.780 --> 00:58:32.610 align:middle line:84% but to argue that, in fact, the world is 00:58:32.610 --> 00:58:36.000 align:middle line:84% made of electromagnetism and mechanics is the after-effect. 00:58:36.000 --> 00:58:38.130 align:middle line:84% It was another wonderful inversion 00:58:38.130 --> 00:58:40.680 align:middle line:84% not just between how we use Maxwell's equations 00:58:40.680 --> 00:58:43.590 align:middle line:84% and them, a kind of distinction over time, 00:58:43.590 --> 00:58:46.690 align:middle line:84% but even at one moment in time a distinction across space. 00:58:46.690 --> 00:58:48.150 align:middle line:84% So I want to sit just a little bit 00:58:48.150 --> 00:58:51.155 align:middle line:84% with these characteristic German approaches-- 00:58:51.155 --> 00:58:52.530 align:middle line:84% again, to get the contrast in how 00:58:52.530 --> 00:58:54.570 align:middle line:84% the same equations could be interpreted 00:58:54.570 --> 00:58:55.780 align:middle line:90% somewhat differently. 00:58:55.780 --> 00:58:59.340 align:middle line:84% So here's a quick example about the origin of mass. 00:58:59.340 --> 00:59:01.290 align:middle line:84% So instead of assuming that objects just 00:59:01.290 --> 00:59:05.310 align:middle line:84% have some mass based on their mechanical composition, 00:59:05.310 --> 00:59:07.230 align:middle line:84% a growing number of these scholars in Germany 00:59:07.230 --> 00:59:11.130 align:middle line:84% asked, what if mass itself-- this prototypical mechanical 00:59:11.130 --> 00:59:15.030 align:middle line:84% property, what if that was an effect of something even more 00:59:15.030 --> 00:59:17.320 align:middle line:90% primary, like electromagnetism? 00:59:17.320 --> 00:59:19.470 align:middle line:84% So let's start with a quick analogy. 00:59:19.470 --> 00:59:23.560 align:middle line:84% Imagine you're trying to drag a beach ball under water. 00:59:23.560 --> 00:59:25.050 align:middle line:84% So think about hydrogen dynamics. 00:59:25.050 --> 00:59:27.840 align:middle line:84% We could describe the kinetic energy of that system. 00:59:27.840 --> 00:59:31.140 align:middle line:84% We'll call the kinetic energy T. If the beach ball has 00:59:31.140 --> 00:59:35.280 align:middle line:84% a mass outside of the medium, some m0, we drag it 00:59:35.280 --> 00:59:38.957 align:middle line:84% with some speed, v, outside the medium, 00:59:38.957 --> 00:59:41.040 align:middle line:84% we could very easily write down the kinetic energy 00:59:41.040 --> 00:59:41.790 align:middle line:90% for that object-- 00:59:41.790 --> 00:59:44.880 align:middle line:90% 1/2 m0 v squared. 00:59:44.880 --> 00:59:46.710 align:middle line:90% We just say the ball has a mass. 00:59:46.710 --> 00:59:48.930 align:middle line:84% It's moving at some velocity whose magnitude 00:59:48.930 --> 00:59:50.940 align:middle line:90% or speed is v. Kinetic energy-- 00:59:50.940 --> 00:59:52.180 align:middle line:90% 1/2 mv squared. 00:59:52.180 --> 00:59:55.470 align:middle line:84% We can actually describe the kinetic energy of the combined 00:59:55.470 --> 00:59:57.840 align:middle line:84% system when the ball is within the medium, when 00:59:57.840 --> 01:00:00.480 align:middle line:84% it's underwater, for an incompressible fluid 01:00:00.480 --> 01:00:04.230 align:middle line:84% like water, by using an effective mass. 01:00:04.230 --> 01:00:08.020 align:middle line:84% We still have an expression that looks like 1/2 mv squared. 01:00:08.020 --> 01:00:10.110 align:middle line:90% But we adjust what we mean by m. 01:00:10.110 --> 01:00:14.010 align:middle line:84% We take into account the mass of the displaced fluid, 01:00:14.010 --> 01:00:15.400 align:middle line:90% in this case. 01:00:15.400 --> 01:00:17.160 align:middle line:84% But otherwise, the form of the equation 01:00:17.160 --> 01:00:18.630 align:middle line:90% is actually still quite tidy. 01:00:18.630 --> 01:00:21.120 align:middle line:90% It's still 1/2 mv squared. 01:00:21.120 --> 01:00:24.570 align:middle line:84% And we adjust the m to take into account that this ball is 01:00:24.570 --> 01:00:26.080 align:middle line:90% displacing some of the fluid. 01:00:26.080 --> 01:00:28.890 align:middle line:84% So its motion, its resistance to change in its motion, 01:00:28.890 --> 01:00:30.990 align:middle line:84% like its mass, is different from what 01:00:30.990 --> 01:00:33.610 align:middle line:90% it would be outside the medium. 01:00:33.610 --> 01:00:36.780 align:middle line:84% So a number of scholars who focused on electromagnetism 01:00:36.780 --> 01:00:40.000 align:middle line:84% in the 1880s and '90s in Germany said, well, 01:00:40.000 --> 01:00:41.700 align:middle line:84% what if that's a useful analogy for what 01:00:41.700 --> 01:00:44.130 align:middle line:90% happens with electric charges? 01:00:44.130 --> 01:00:46.620 align:middle line:84% So imagine the motion of a single object 01:00:46.620 --> 01:00:49.470 align:middle line:84% that has some charge Q, some electric charge. 01:00:49.470 --> 01:00:51.750 align:middle line:84% By virtue of having some electric charge, 01:00:51.750 --> 01:00:54.300 align:middle line:84% it necessarily is creating an electric field, 01:00:54.300 --> 01:00:56.550 align:middle line:84% some disturbance in the local ether. 01:00:56.550 --> 01:00:59.730 align:middle line:84% Moreover, if that charge is moving with some velocity, 01:00:59.730 --> 01:01:03.150 align:middle line:84% it is by necessity generating some magnetic effects. 01:01:03.150 --> 01:01:07.320 align:middle line:84% There is an induced magnetic field from a charge in motion. 01:01:07.320 --> 01:01:09.570 align:middle line:84% And there is an electric field associated 01:01:09.570 --> 01:01:12.030 align:middle line:84% with the electric charge, even if it's at rest. 01:01:12.030 --> 01:01:14.550 align:middle line:84% So electric and magnetic fields will 01:01:14.550 --> 01:01:17.370 align:middle line:84% affect the motion of an object with electric charge. 01:01:17.370 --> 01:01:19.110 align:middle line:84% So the question was to consider what 01:01:19.110 --> 01:01:21.420 align:middle line:84% we might now call the back-reaction 01:01:21.420 --> 01:01:23.640 align:middle line:90% or the self-field effects. 01:01:23.640 --> 01:01:26.760 align:middle line:84% How can we characterize the motion of an electric charge 01:01:26.760 --> 01:01:29.340 align:middle line:84% in its own electric and magnetic fields-- 01:01:29.340 --> 01:01:33.920 align:middle line:84% not external fields that we host separately, but by virtue 01:01:33.920 --> 01:01:35.600 align:middle line:84% of the fact that an electric an object 01:01:35.600 --> 01:01:37.820 align:middle line:84% with some electric charge by necessity 01:01:37.820 --> 01:01:40.550 align:middle line:84% creates an electric and a magnetic field if it's moving? 01:01:40.550 --> 01:01:43.760 align:middle line:84% And those should act back on its own motion. 01:01:43.760 --> 01:01:46.550 align:middle line:84% So you could consider something like the Lorentz force law. 01:01:46.550 --> 01:01:49.370 align:middle line:84% The force, therefore the changes in that charged object's 01:01:49.370 --> 01:01:54.710 align:middle line:84% motion, will be due to the electric field and its velocity 01:01:54.710 --> 01:01:56.910 align:middle line:84% cross-product into the magnetic field. 01:01:56.910 --> 01:01:58.670 align:middle line:84% Now, what if these are the self-fields 01:01:58.670 --> 01:02:00.050 align:middle line:90% of that charged object? 01:02:00.050 --> 01:02:03.260 align:middle line:84% You can do the same, trick they found quite cleverly. 01:02:03.260 --> 01:02:07.070 align:middle line:84% You can still characterize the kinetic energy of that system 01:02:07.070 --> 01:02:09.380 align:middle line:90% as 1/2 mv squared. 01:02:09.380 --> 01:02:11.330 align:middle line:84% Just like that beach ball underwater, 01:02:11.330 --> 01:02:13.280 align:middle line:90% we make an effective mass. 01:02:13.280 --> 01:02:16.430 align:middle line:84% We take into account the extra mass 01:02:16.430 --> 01:02:19.880 align:middle line:84% that comes from these field effects that 01:02:19.880 --> 01:02:22.190 align:middle line:84% will impact how quickly that charged 01:02:22.190 --> 01:02:24.470 align:middle line:84% object would change its motion due 01:02:24.470 --> 01:02:26.450 align:middle line:90% to a different imposed force. 01:02:26.450 --> 01:02:28.610 align:middle line:84% That's why the mass is a measure of its resistance 01:02:28.610 --> 01:02:30.240 align:middle line:90% to changes its motion. 01:02:30.240 --> 01:02:32.243 align:middle line:90% It's just 1/2 mv squared. 01:02:32.243 --> 01:02:33.660 align:middle line:84% And there's a different expression 01:02:33.660 --> 01:02:35.700 align:middle line:84% for the effective mass that comes 01:02:35.700 --> 01:02:38.820 align:middle line:84% uniquely from this kind of back-reaction 01:02:38.820 --> 01:02:40.860 align:middle line:90% of its self-fields. 01:02:40.860 --> 01:02:42.960 align:middle line:84% And the calculator is a tour de force. 01:02:42.960 --> 01:02:47.220 align:middle line:84% You can calculate it based on the properties of that system. 01:02:47.220 --> 01:02:49.560 align:middle line:84% Unlike the beach ball underwater though-- 01:02:49.560 --> 01:02:51.630 align:middle line:84% this is the next step that many of them took-- 01:02:51.630 --> 01:02:54.900 align:middle line:84% the electric charge can never be taken outside of this medium. 01:02:54.900 --> 01:02:57.900 align:middle line:84% You can't turn off its own electric field if it still 01:02:57.900 --> 01:02:59.160 align:middle line:90% has some electric charge. 01:02:59.160 --> 01:03:00.810 align:middle line:84% If it's moving, you can't stop it 01:03:00.810 --> 01:03:03.280 align:middle line:84% from generating some magnetic field. 01:03:03.280 --> 01:03:05.640 align:middle line:84% So unlike the beach ball, you can never 01:03:05.640 --> 01:03:08.160 align:middle line:84% take this electric charge out of this medium 01:03:08.160 --> 01:03:10.890 align:middle line:90% of these self-fields. 01:03:10.890 --> 01:03:14.700 align:middle line:84% As a next step they take, what if there is no mechanical mass? 01:03:14.700 --> 01:03:17.430 align:middle line:84% What if this what we might call a bare mass 01:03:17.430 --> 01:03:20.100 align:middle line:90% or mechanical mass vanished? 01:03:20.100 --> 01:03:23.050 align:middle line:84% What if all mass always arose from 01:03:23.050 --> 01:03:24.300 align:middle line:90% these electromagnetic effects? 01:03:24.300 --> 01:03:27.390 align:middle line:84% That's what I mean by them turning it on its head. 01:03:27.390 --> 01:03:30.310 align:middle line:84% So all of mechanics, in their estimation, 01:03:30.310 --> 01:03:34.200 align:middle line:84% might arise from these complicated effects 01:03:34.200 --> 01:03:36.090 align:middle line:84% of electric and magnetic fields, including 01:03:36.090 --> 01:03:38.580 align:middle line:84% the self-fields from these objects skittering 01:03:38.580 --> 01:03:40.360 align:middle line:90% through space on their own. 01:03:40.360 --> 01:03:43.350 align:middle line:84% So one of the very influential proponents of this view, 01:03:43.350 --> 01:03:46.290 align:middle line:84% Wilhelm Wien, announced, in 1900, this 01:03:46.290 --> 01:03:50.160 align:middle line:84% presents the possibility of an electromagnetic foundation 01:03:50.160 --> 01:03:51.150 align:middle line:90% for mechanics. 01:03:51.150 --> 01:03:53.638 align:middle line:84% This, again, became known as an electromagnetic worldview. 01:03:53.638 --> 01:03:55.680 align:middle line:84% And I hope you can see that's a kind of inversion 01:03:55.680 --> 01:03:58.140 align:middle line:84% from the British mechanical worldview, where 01:03:58.140 --> 01:04:01.740 align:middle line:84% all the electromagnetic effects the British folks often were 01:04:01.740 --> 01:04:06.090 align:middle line:84% convinced arose from mechanical stresses and strains. 01:04:06.090 --> 01:04:08.070 align:middle line:84% Now, a number of these German scholars 01:04:08.070 --> 01:04:09.870 align:middle line:84% said, what if actually mechanics, 01:04:09.870 --> 01:04:13.933 align:middle line:84% like F equals ma, is actually coming from electromagnetism? 01:04:13.933 --> 01:04:15.100 align:middle line:90% So I'm going to pause there. 01:04:15.100 --> 01:04:16.642 align:middle line:84% Again, I'll stop sharing screen, just 01:04:16.642 --> 01:04:19.620 align:middle line:84% to give a quick taste for how, even in their own day, 01:04:19.620 --> 01:04:23.040 align:middle line:84% Maxwell's equations, again, could 01:04:23.040 --> 01:04:24.750 align:middle line:84% inspire other interpretations, even when 01:04:24.750 --> 01:04:26.430 align:middle line:90% they use the same equations. 01:04:26.430 --> 01:04:27.640 align:middle line:90% Any questions on that stuff? 01:04:27.640 --> 01:04:35.990 align:middle line:90% 01:04:35.990 --> 01:04:36.628 align:middle line:90% OK. 01:04:36.628 --> 01:04:39.170 align:middle line:84% If other questions come up, feel free to put them in the chat 01:04:39.170 --> 01:04:39.962 align:middle line:90% or raise your hand. 01:04:39.962 --> 01:04:41.160 align:middle line:90% But if not, I'll press on. 01:04:41.160 --> 01:04:43.640 align:middle line:84% The last main section for the lecture, almost done. 01:04:43.640 --> 01:04:45.260 align:middle line:84% For the last part, I want to get back 01:04:45.260 --> 01:04:47.000 align:middle line:84% to some of the institutional questions. 01:04:47.000 --> 01:04:49.610 align:middle line:84% Where were some of these German scholars doing their work 01:04:49.610 --> 01:04:50.240 align:middle line:90% and why? 01:04:50.240 --> 01:04:53.060 align:middle line:84% So we're going to have another contrast, German and Britain, 01:04:53.060 --> 01:04:55.820 align:middle line:84% not only conceptually, but now also in 01:04:55.820 --> 01:04:58.640 align:middle line:84% terms of the types of places and the types of priorities 01:04:58.640 --> 01:05:01.040 align:middle line:84% in which these folks were conducting their research. 01:05:01.040 --> 01:05:04.640 align:middle line:84% So the last main part for today is now this question 01:05:04.640 --> 01:05:07.170 align:middle line:90% about institutions. 01:05:07.170 --> 01:05:09.860 align:middle line:84% So what does it mean to have a job title 01:05:09.860 --> 01:05:11.300 align:middle line:90% theoretical physicist? 01:05:11.300 --> 01:05:14.000 align:middle line:84% When does that become something that people could aspire 01:05:14.000 --> 01:05:16.140 align:middle line:90% to, let alone get paid to do? 01:05:16.140 --> 01:05:19.280 align:middle line:84% It's not in the age of Galileo or Newton. 01:05:19.280 --> 01:05:22.190 align:middle line:84% So some of the folks whose work we would inherit, 01:05:22.190 --> 01:05:25.520 align:middle line:84% we would consider part of the theoretical physics legacy 01:05:25.520 --> 01:05:27.223 align:middle line:84% was done by people who were never 01:05:27.223 --> 01:05:28.640 align:middle line:84% in their own time called something 01:05:28.640 --> 01:05:30.260 align:middle line:90% theoretical physicist. 01:05:30.260 --> 01:05:32.450 align:middle line:84% In their own time, in the early and even 01:05:32.450 --> 01:05:35.120 align:middle line:84% through the late 1600s, these folks 01:05:35.120 --> 01:05:36.660 align:middle line:84% were either called mathematician-- 01:05:36.660 --> 01:05:39.240 align:middle line:84% that was a term that's recognized-- or philosopher, 01:05:39.240 --> 01:05:42.490 align:middle line:84% or more broadly natural philosopher, as we saw. 01:05:42.490 --> 01:05:45.540 align:middle line:84% So the Galileo, Newton, 17th century stuff, 01:05:45.540 --> 01:05:48.690 align:middle line:84% there just simply did not exist a person whose job title 01:05:48.690 --> 01:05:50.050 align:middle line:90% was theoretical physicist. 01:05:50.050 --> 01:05:50.550 align:middle line:90% OK. 01:05:50.550 --> 01:05:51.675 align:middle line:90% Let's move forward in time. 01:05:51.675 --> 01:05:53.620 align:middle line:90% What, about in the 18th century? 01:05:53.620 --> 01:05:55.530 align:middle line:84% People like Lagrange, or Laplace, 01:05:55.530 --> 01:05:57.660 align:middle line:84% or Euler, or any of these other folks 01:05:57.660 --> 01:06:00.570 align:middle line:84% whose work we still use so much today? 01:06:00.570 --> 01:06:02.610 align:middle line:84% Again, they were doing work that we 01:06:02.610 --> 01:06:05.688 align:middle line:84% have folded into the activity of theoretical physics. 01:06:05.688 --> 01:06:07.230 align:middle line:84% We couldn't do our work without them, 01:06:07.230 --> 01:06:09.730 align:middle line:84% thinking about lagrangians, for those of you who've seen it, 01:06:09.730 --> 01:06:11.190 align:middle line:90% or the laplacian operator. 01:06:11.190 --> 01:06:14.760 align:middle line:84% We use their work all the time in theoretical physics. 01:06:14.760 --> 01:06:17.310 align:middle line:84% They were, again, called mathematicians or often 01:06:17.310 --> 01:06:18.150 align:middle line:90% astronomers. 01:06:18.150 --> 01:06:20.940 align:middle line:84% Now, that term was often now in common usage. 01:06:20.940 --> 01:06:24.248 align:middle line:84% They were not called theoretical physicists. 01:06:24.248 --> 01:06:26.040 align:middle line:84% What about someone like James Clerk Maxwell 01:06:26.040 --> 01:06:29.080 align:middle line:84% now by the mid to late 19th century, 01:06:29.080 --> 01:06:31.330 align:middle line:84% during the period we've been focusing on in this class 01:06:31.330 --> 01:06:31.890 align:middle line:90% so far? 01:06:31.890 --> 01:06:35.240 align:middle line:90% 01:06:35.240 --> 01:06:38.210 align:middle line:84% By Maxwell's day, the term physicist 01:06:38.210 --> 01:06:39.680 align:middle line:90% had become much more common. 01:06:39.680 --> 01:06:43.160 align:middle line:84% That was a kind of job title, not theoretical physicist. 01:06:43.160 --> 01:06:44.780 align:middle line:84% And indeed, still natural philosopher 01:06:44.780 --> 01:06:47.060 align:middle line:90% was not uncommon either. 01:06:47.060 --> 01:06:50.990 align:middle line:84% So a lot of the work that we would recognize as core 01:06:50.990 --> 01:06:54.710 align:middle line:84% to the job of a theoretical physicist, to the toolkit, 01:06:54.710 --> 01:06:57.980 align:middle line:84% was done by people who did not have that job title 01:06:57.980 --> 01:07:01.370 align:middle line:84% and would not probably have even recognized it in their day. 01:07:01.370 --> 01:07:05.630 align:middle line:84% The term and the associated role in society 01:07:05.630 --> 01:07:07.700 align:middle line:84% of theoretical physicists comes out 01:07:07.700 --> 01:07:10.310 align:middle line:84% of a very particular moment in the middle decades 01:07:10.310 --> 01:07:12.980 align:middle line:84% of the 19th century, that same period of these reforms 01:07:12.980 --> 01:07:15.290 align:middle line:84% at Cambridge, and these cool things with radial waves, 01:07:15.290 --> 01:07:16.080 align:middle line:90% and all that. 01:07:16.080 --> 01:07:19.410 align:middle line:84% And here, it really comes out of the German system. 01:07:19.410 --> 01:07:23.870 align:middle line:84% So take just a few moments to think about this very unusual 01:07:23.870 --> 01:07:26.507 align:middle line:84% and, let's say, peculiar German university system. 01:07:26.507 --> 01:07:28.340 align:middle line:84% And here, I'm drawing especially on the work 01:07:28.340 --> 01:07:30.380 align:middle line:90% by a pair of historians. 01:07:30.380 --> 01:07:32.790 align:middle line:84% They wrote another two-volume book. 01:07:32.790 --> 01:07:35.160 align:middle line:84% This one is only about 600 pages altogether, 01:07:35.160 --> 01:07:38.100 align:middle line:84% not 900 pages, a quite fascinating book 01:07:38.100 --> 01:07:41.100 align:middle line:84% by Christa Jungnickel and Russell McCormmach. 01:07:41.100 --> 01:07:43.410 align:middle line:84% So one thing to keep in mind is especially 01:07:43.410 --> 01:07:47.370 align:middle line:84% after Germany became one unified country in 1871, 01:07:47.370 --> 01:07:50.460 align:middle line:84% there was a central education ministry. 01:07:50.460 --> 01:07:52.260 align:middle line:84% So within the entire country, there 01:07:52.260 --> 01:07:56.100 align:middle line:84% was one basically central government bureau 01:07:56.100 --> 01:07:59.680 align:middle line:84% that assigned all the senior professors in every field, 01:07:59.680 --> 01:08:03.333 align:middle line:84% in every university, a central bureau that doled out or made 01:08:03.333 --> 01:08:06.000 align:middle line:84% the assignments for who would be the full professor in the field 01:08:06.000 --> 01:08:08.820 align:middle line:84% of physics, or philosophy, or history, or theology, 01:08:08.820 --> 01:08:11.490 align:middle line:90% or chemistry, or anything. 01:08:11.490 --> 01:08:13.750 align:middle line:84% Moreover, in each of these universities, 01:08:13.750 --> 01:08:16.080 align:middle line:84% there was one full professor who was 01:08:16.080 --> 01:08:19.450 align:middle line:84% called the ordinarius professor in a given field. 01:08:19.450 --> 01:08:21.930 align:middle line:84% So it would be one full professor of physics 01:08:21.930 --> 01:08:24.149 align:middle line:90% at, say, Wurzburg University. 01:08:24.149 --> 01:08:26.819 align:middle line:84% There'd be one full, or ordinarius, professor 01:08:26.819 --> 01:08:29.760 align:middle line:84% of physics in Berlin, and so on, assigned 01:08:29.760 --> 01:08:33.180 align:middle line:84% by the central bureau, one full professor per subject 01:08:33.180 --> 01:08:34.410 align:middle line:90% per university. 01:08:34.410 --> 01:08:36.630 align:middle line:84% In the case of physics, the ordinarius, 01:08:36.630 --> 01:08:38.729 align:middle line:84% or the single full professor, was 01:08:38.729 --> 01:08:41.490 align:middle line:84% in charge of all the apparatus in the department, all 01:08:41.490 --> 01:08:42.520 align:middle line:90% the experimental work. 01:08:42.520 --> 01:08:45.390 align:middle line:84% Here's an example of Wilhelm Rankin's laboratory 01:08:45.390 --> 01:08:46.830 align:middle line:90% in the 1890s, for example. 01:08:46.830 --> 01:08:48.720 align:middle line:90% Rankin was the ordinarius. 01:08:48.720 --> 01:08:52.020 align:middle line:84% This stuff was often treated as if it was the personal property 01:08:52.020 --> 01:08:53.550 align:middle line:90% of that one head professor. 01:08:53.550 --> 01:08:55.350 align:middle line:84% This was basically Rankin's property 01:08:55.350 --> 01:08:57.300 align:middle line:90% until Rankin retired or died. 01:08:57.300 --> 01:09:00.479 align:middle line:84% And then it would bequeathed to the next ordinarius 01:09:00.479 --> 01:09:01.620 align:middle line:90% professor of physics. 01:09:01.620 --> 01:09:03.450 align:middle line:84% So the one head full professor was 01:09:03.450 --> 01:09:05.880 align:middle line:84% in charge of all the experimental equipment. 01:09:05.880 --> 01:09:08.010 align:middle line:84% What it meant to be a physics professor 01:09:08.010 --> 01:09:09.990 align:middle line:84% was to be an experimental physicist. 01:09:09.990 --> 01:09:11.790 align:middle line:84% And the way you demonstrated that was 01:09:11.790 --> 01:09:14.160 align:middle line:84% by being the ordinarius in charge of all the equipment. 01:09:14.160 --> 01:09:17.609 align:middle line:84% After Germany became one unified country, after its war 01:09:17.609 --> 01:09:22.109 align:middle line:84% with France, the country really accelerated a very rapid period 01:09:22.109 --> 01:09:24.930 align:middle line:84% of industrialization, very large scale industrialization. 01:09:24.930 --> 01:09:28.410 align:middle line:84% They thought they were behind both Britain and France. 01:09:28.410 --> 01:09:30.270 align:middle line:84% They began investing very heavily 01:09:30.270 --> 01:09:34.580 align:middle line:84% in what we might consider many areas of engineering. 01:09:34.580 --> 01:09:37.069 align:middle line:84% For that, they needed a large, large number 01:09:37.069 --> 01:09:39.240 align:middle line:84% of physics teachers-- not only for universities, 01:09:39.240 --> 01:09:41.720 align:middle line:84% but especially for things like the high schools. 01:09:41.720 --> 01:09:44.060 align:middle line:84% They needed many folks who could go into and help 01:09:44.060 --> 01:09:48.080 align:middle line:84% design and improve these massive public works projects. 01:09:48.080 --> 01:09:51.229 align:middle line:84% They needed lots and lots of people who could teach physics 01:09:51.229 --> 01:09:53.430 align:middle line:90% at the high school level. 01:09:53.430 --> 01:09:55.670 align:middle line:84% So the classrooms grow very rapidly. 01:09:55.670 --> 01:09:57.830 align:middle line:84% So then you have to hire lots of people 01:09:57.830 --> 01:10:00.900 align:middle line:84% to teach all those would-be high school teachers. 01:10:00.900 --> 01:10:04.130 align:middle line:84% So there's a huge growth at the universities throughout Germany 01:10:04.130 --> 01:10:05.930 align:middle line:90% in extra faculty. 01:10:05.930 --> 01:10:08.120 align:middle line:84% They were called extraordinarius not because they 01:10:08.120 --> 01:10:10.130 align:middle line:90% were extraordinary. 01:10:10.130 --> 01:10:11.750 align:middle line:90% It's like a false cognate. 01:10:11.750 --> 01:10:14.810 align:middle line:84% These were extra, in addition to, the ordinarius. 01:10:14.810 --> 01:10:15.920 align:middle line:90% So these were lower rank. 01:10:15.920 --> 01:10:18.920 align:middle line:84% These were like junior faculty in our modern parlance. 01:10:18.920 --> 01:10:20.420 align:middle line:84% They were not tenured, many of them. 01:10:20.420 --> 01:10:22.503 align:middle line:84% They certainly were not the single full professor. 01:10:22.503 --> 01:10:25.940 align:middle line:84% You staff up lots of extra to the ordinarius, lots 01:10:25.940 --> 01:10:28.430 align:middle line:84% of junior faculty at universities 01:10:28.430 --> 01:10:29.960 align:middle line:84% to teach lots of physics because you 01:10:29.960 --> 01:10:31.580 align:middle line:84% need to get lots of high school teachers who 01:10:31.580 --> 01:10:33.800 align:middle line:84% could teach even more people basic physics, math, 01:10:33.800 --> 01:10:36.140 align:middle line:90% and even engineering. 01:10:36.140 --> 01:10:39.590 align:middle line:84% Now, these younger faculty, these extraordinarius faculty, 01:10:39.590 --> 01:10:41.720 align:middle line:84% only have access to pencil and paper. 01:10:41.720 --> 01:10:43.355 align:middle line:84% They're not in charge of the equipment. 01:10:43.355 --> 01:10:44.480 align:middle line:90% They're not the ordinarius. 01:10:44.480 --> 01:10:46.320 align:middle line:84% It's not their personal property. 01:10:46.320 --> 01:10:49.160 align:middle line:84% So all they can do is push pencils around on paper. 01:10:49.160 --> 01:10:51.145 align:middle line:84% Here's an example of one of them at one stage 01:10:51.145 --> 01:10:53.520 align:middle line:84% in his career, Einstein, a person we'll spend quite a bit 01:10:53.520 --> 01:10:54.570 align:middle line:90% of time talking about. 01:10:54.570 --> 01:10:56.460 align:middle line:84% Well before Einstein was scribbling 01:10:56.460 --> 01:10:59.400 align:middle line:84% in his Zurich notebook in 1912, really 01:10:59.400 --> 01:11:03.000 align:middle line:84% starting in earnest in the 1850s, '60s, and '70s, 01:11:03.000 --> 01:11:06.120 align:middle line:84% you have lots and lots of people who are now joining the faculty 01:11:06.120 --> 01:11:09.930 align:middle line:84% ranks at this lower level, this extraordinarius level. 01:11:09.930 --> 01:11:11.475 align:middle line:84% They don't have access, in general, 01:11:11.475 --> 01:11:13.350 align:middle line:84% to the experimental equipment, unless they're 01:11:13.350 --> 01:11:15.270 align:middle line:84% in the good graces of the full professor. 01:11:15.270 --> 01:11:16.710 align:middle line:90% They can't control it. 01:11:16.710 --> 01:11:19.380 align:middle line:84% So they spend most of their time in research 01:11:19.380 --> 01:11:21.870 align:middle line:84% doing pencil and paper work, mathematical work. 01:11:21.870 --> 01:11:23.850 align:middle line:84% Once you build up lots of folks who 01:11:23.850 --> 01:11:25.950 align:middle line:84% have done that for one or two generations, 01:11:25.950 --> 01:11:27.840 align:middle line:90% there becomes a kind of norm. 01:11:27.840 --> 01:11:30.630 align:middle line:84% There becomes a kind of community 01:11:30.630 --> 01:11:33.280 align:middle line:84% that's really good at mathematical or theoretical 01:11:33.280 --> 01:11:33.780 align:middle line:90% physics. 01:11:33.780 --> 01:11:36.360 align:middle line:84% It starts sounding like the Cambridge story. 01:11:36.360 --> 01:11:38.670 align:middle line:84% If you push lots of people through the Mathematical 01:11:38.670 --> 01:11:40.950 align:middle line:84% Tripos, some portion will get very good 01:11:40.950 --> 01:11:43.770 align:middle line:84% at mathematical analysis for physics. 01:11:43.770 --> 01:11:45.990 align:middle line:84% A similar thing for different reasons 01:11:45.990 --> 01:11:48.250 align:middle line:84% is happening around the same time, 01:11:48.250 --> 01:11:51.240 align:middle line:84% especially in the united German university systems 01:11:51.240 --> 01:11:53.730 align:middle line:84% now because this quirky university structure, 01:11:53.730 --> 01:11:56.520 align:middle line:84% where you have a very tightly controlled, full professor 01:11:56.520 --> 01:11:57.270 align:middle line:90% rank. 01:11:57.270 --> 01:11:59.310 align:middle line:84% You have extraordinary people who 01:11:59.310 --> 01:12:02.670 align:middle line:84% can't do as much experimental work as they might like. 01:12:02.670 --> 01:12:06.487 align:middle line:84% But they get really good at showing their own command 01:12:06.487 --> 01:12:08.820 align:middle line:84% of theoretical physics because they spend all their time 01:12:08.820 --> 01:12:10.210 align:middle line:90% with pencil and paper. 01:12:10.210 --> 01:12:13.050 align:middle line:84% So only by the end of that 19th century 01:12:13.050 --> 01:12:15.060 align:middle line:84% do some universities begin to recognize 01:12:15.060 --> 01:12:16.620 align:middle line:90% this is now a new thing. 01:12:16.620 --> 01:12:19.470 align:middle line:84% And there are finally ordinarius professorships, 01:12:19.470 --> 01:12:22.140 align:middle line:84% full professorships made for theoretical physics. 01:12:22.140 --> 01:12:24.240 align:middle line:84% So increasing numbers of universities 01:12:24.240 --> 01:12:26.070 align:middle line:84% within this German system would then 01:12:26.070 --> 01:12:28.530 align:middle line:84% have two full professors of physics-- 01:12:28.530 --> 01:12:31.530 align:middle line:84% the ordinarius in charge of the experimental work 01:12:31.530 --> 01:12:35.340 align:middle line:84% and now a second ordinarius in charge of theoretical physics. 01:12:35.340 --> 01:12:37.770 align:middle line:84% The very first to be assigned to in that 01:12:37.770 --> 01:12:41.730 align:middle line:84% role was Gustav Kirchhoff, whose work is still well-known to us 01:12:41.730 --> 01:12:44.490 align:middle line:84% from things like thermodynamics and statistical physics. 01:12:44.490 --> 01:12:46.290 align:middle line:84% A few years later, Max Planck became 01:12:46.290 --> 01:12:48.780 align:middle line:84% one of the earliest ordinarius professors 01:12:48.780 --> 01:12:50.908 align:middle line:84% of theoretical physics in Berlin. 01:12:50.908 --> 01:12:52.950 align:middle line:84% They start their own journals because there's now 01:12:52.950 --> 01:12:55.642 align:middle line:84% a kind of specialty community, their own editors 01:12:55.642 --> 01:12:56.850 align:middle line:90% of their specialist journals. 01:12:56.850 --> 01:13:00.660 align:middle line:84% So again, we start getting a job title of theoretical physics 01:13:00.660 --> 01:13:02.790 align:middle line:84% not because there's an aim to make let's make 01:13:02.790 --> 01:13:04.200 align:middle line:90% more theoretical physicists. 01:13:04.200 --> 01:13:06.330 align:middle line:84% There's an aim, in the German case, 01:13:06.330 --> 01:13:08.730 align:middle line:84% to have a very rapid acceleration 01:13:08.730 --> 01:13:11.190 align:middle line:90% of nationwide industrialization. 01:13:11.190 --> 01:13:14.610 align:middle line:84% And partly how that plays out, in this very unusual university 01:13:14.610 --> 01:13:19.020 align:middle line:84% system, is to bloat the early or middle ranks of faculty. 01:13:19.020 --> 01:13:22.470 align:middle line:84% And that diverts them, more often than not, 01:13:22.470 --> 01:13:24.720 align:middle line:84% to one kind of research rather than another. 01:13:24.720 --> 01:13:28.500 align:middle line:84% Do that after a while, and there coalesces a recognized set 01:13:28.500 --> 01:13:32.580 align:middle line:84% of standards and even a kind of job title for the strange thing 01:13:32.580 --> 01:13:34.530 align:middle line:90% called a theoretical physicist. 01:13:34.530 --> 01:13:36.030 align:middle line:84% Now, the last few slides to wrap up, 01:13:36.030 --> 01:13:38.110 align:middle line:84% then we'll have time for some more questions. 01:13:38.110 --> 01:13:41.730 align:middle line:84% So in place of this British empire building as one 01:13:41.730 --> 01:13:43.830 align:middle line:84% of the main roots to building up this community 01:13:43.830 --> 01:13:46.770 align:middle line:84% of mathematically trained mathematical or theoretical 01:13:46.770 --> 01:13:48.870 align:middle line:84% physicists-- we think about that Tripos exam-- 01:13:48.870 --> 01:13:51.900 align:middle line:84% in the newly unified country of Germany, 01:13:51.900 --> 01:13:54.000 align:middle line:84% the field of theoretical physics takes root 01:13:54.000 --> 01:13:55.980 align:middle line:90% in a pretty different context. 01:13:55.980 --> 01:13:57.130 align:middle line:90% The timing is similar. 01:13:57.130 --> 01:13:59.860 align:middle line:84% But the drivers are actually a bit different. 01:13:59.860 --> 01:14:03.840 align:middle line:84% There's this very centrally controlled university system, 01:14:03.840 --> 01:14:06.840 align:middle line:84% very tight limit on the highest ranking positions. 01:14:06.840 --> 01:14:09.720 align:middle line:84% And for the field of physics in particular, the ordinarius, 01:14:09.720 --> 01:14:12.120 align:middle line:84% or full professors, was coextensive 01:14:12.120 --> 01:14:13.320 align:middle line:90% with experimental physics. 01:14:13.320 --> 01:14:16.650 align:middle line:84% That's what it meant to be a physics professor. 01:14:16.650 --> 01:14:19.290 align:middle line:84% Changing industrialization changes the priorities. 01:14:19.290 --> 01:14:21.990 align:middle line:84% You need lots of people who can do at least rudimentary physics 01:14:21.990 --> 01:14:24.122 align:middle line:84% and mathematics to help with their engineering. 01:14:24.122 --> 01:14:26.580 align:middle line:84% You need lots of people who can teach them in high schools. 01:14:26.580 --> 01:14:27.997 align:middle line:84% Therefore, you need lots of people 01:14:27.997 --> 01:14:30.880 align:middle line:84% who can teach the teachers at the universities, and so on. 01:14:30.880 --> 01:14:33.640 align:middle line:84% So within a generation or two, you 01:14:33.640 --> 01:14:36.310 align:middle line:84% create this spillover effect, where 01:14:36.310 --> 01:14:38.560 align:middle line:84% you have ordinary professors, and journals, 01:14:38.560 --> 01:14:40.000 align:middle line:84% and specialists in this new thing 01:14:40.000 --> 01:14:41.125 align:middle line:90% called theoretical physics. 01:14:41.125 --> 01:14:42.700 align:middle line:90% Why do I emphasize all that? 01:14:42.700 --> 01:14:44.950 align:middle line:84% Because it's in that very particular 01:14:44.950 --> 01:14:47.260 align:middle line:84% institutional context, within Germany 01:14:47.260 --> 01:14:52.080 align:middle line:84% in the later decades of the 1800s and early 20th century, 01:14:52.080 --> 01:14:53.830 align:middle line:84% that's where a lot of the stuff that we're 01:14:53.830 --> 01:14:57.040 align:middle line:84% sitting with for the next few weeks of our class, 01:14:57.040 --> 01:14:59.530 align:middle line:84% the emergence of what we come to call modern physics, 01:14:59.530 --> 01:15:01.750 align:middle line:84% like relativity and quantum theory-- 01:15:01.750 --> 01:15:05.050 align:middle line:84% a lot of that is being crafted in that particular 01:15:05.050 --> 01:15:06.217 align:middle line:90% institutional context. 01:15:06.217 --> 01:15:08.050 align:middle line:84% We want to understand why there was suddenly 01:15:08.050 --> 01:15:11.110 align:middle line:84% an ordinarius chair in theoretical physics in Berlin 01:15:11.110 --> 01:15:12.110 align:middle line:90% and so on. 01:15:12.110 --> 01:15:13.870 align:middle line:84% So I just want to give us an indication 01:15:13.870 --> 01:15:16.360 align:middle line:84% that theoretical physics intellectually has 01:15:16.360 --> 01:15:18.250 align:middle line:90% a many centuries lineage. 01:15:18.250 --> 01:15:20.710 align:middle line:84% We can trace back why we still use 01:15:20.710 --> 01:15:23.330 align:middle line:84% the Galilean transformations or Newton's laws. 01:15:23.330 --> 01:15:25.630 align:middle line:84% And yet, the job title, or the description, 01:15:25.630 --> 01:15:27.790 align:middle line:84% of the theoretical physicist is actually 01:15:27.790 --> 01:15:29.260 align:middle line:90% much more recent vintage. 01:15:29.260 --> 01:15:31.332 align:middle line:84% So I'll stop my screen sharing there. 01:15:31.332 --> 01:15:33.290 align:middle line:84% We have a couple of minutes for some questions, 01:15:33.290 --> 01:15:34.915 align:middle line:84% if people have other questions on that. 01:15:34.915 --> 01:15:38.530 align:middle line:90% 01:15:38.530 --> 01:15:39.370 align:middle line:90% Great question. 01:15:39.370 --> 01:15:40.120 align:middle line:90% Thank you, Fisher. 01:15:40.120 --> 01:15:42.070 align:middle line:90% So you're very much correct. 01:15:42.070 --> 01:15:44.860 align:middle line:84% There was a lot of tension factors. 01:15:44.860 --> 01:15:46.967 align:middle line:84% Of course, we now know what's on the horizon-- 01:15:46.967 --> 01:15:47.800 align:middle line:90% the First World War. 01:15:47.800 --> 01:15:49.842 align:middle line:84% And of course, there were many, many quite bloody 01:15:49.842 --> 01:15:52.640 align:middle line:84% skirmishes and wars even before that. 01:15:52.640 --> 01:15:55.493 align:middle line:84% So on the one hand, there was a lot of nation-based rivalry. 01:15:55.493 --> 01:15:57.160 align:middle line:84% The Germans looked over their shoulders, 01:15:57.160 --> 01:16:01.660 align:middle line:84% the German bureaucrats at least, German government officials, 01:16:01.660 --> 01:16:04.000 align:middle line:84% and were scared out of their wits 01:16:04.000 --> 01:16:06.438 align:middle line:84% that they beat the French in 1870, '71, 01:16:06.438 --> 01:16:07.730 align:middle line:90% but they'll lose the next time. 01:16:07.730 --> 01:16:10.430 align:middle line:84% Or the British Navy is second to none. 01:16:10.430 --> 01:16:12.070 align:middle line:84% So they're always comparing themselves 01:16:12.070 --> 01:16:15.430 align:middle line:84% in terms of industrial output and military strength, mostly 01:16:15.430 --> 01:16:18.130 align:middle line:84% in this period with Britain and France, 01:16:18.130 --> 01:16:21.280 align:middle line:84% also increasingly Russia and other neighbors. 01:16:21.280 --> 01:16:22.930 align:middle line:90% So there's a lot of the rivalry. 01:16:22.930 --> 01:16:24.580 align:middle line:84% That spills over not infrequently 01:16:24.580 --> 01:16:25.750 align:middle line:90% among the scientists. 01:16:25.750 --> 01:16:27.940 align:middle line:84% This is also, however, the first period 01:16:27.940 --> 01:16:32.260 align:middle line:84% of international scientific conferences. 01:16:32.260 --> 01:16:35.170 align:middle line:84% The natural researchers, the professional researchers, 01:16:35.170 --> 01:16:39.230 align:middle line:84% starting in the 1870s, would begin to meet once a year, 01:16:39.230 --> 01:16:42.590 align:middle line:84% or twice, or three times a year for conferences 01:16:42.590 --> 01:16:44.990 align:middle line:84% in what we would now consider quite familiar. 01:16:44.990 --> 01:16:47.510 align:middle line:84% That was new, mostly in the 1870s. 01:16:47.510 --> 01:16:49.605 align:middle line:84% They would work out things like nomenclature. 01:16:49.605 --> 01:16:51.230 align:middle line:84% That's why so many things were actually 01:16:51.230 --> 01:16:52.790 align:middle line:84% still named in Latin, even though no one was 01:16:52.790 --> 01:16:53.570 align:middle line:90% speaking Latin. 01:16:53.570 --> 01:16:58.220 align:middle line:84% They wanted to find some way to share ideas and terms 01:16:58.220 --> 01:16:59.540 align:middle line:90% for things and work it out. 01:16:59.540 --> 01:17:02.210 align:middle line:84% So it was sometimes a kind of friendly rivalry. 01:17:02.210 --> 01:17:03.660 align:middle line:84% Sometimes, it wasn't so friendly. 01:17:03.660 --> 01:17:05.540 align:middle line:90% So you see elements of both. 01:17:05.540 --> 01:17:09.200 align:middle line:84% And you're quite right, Fisher, this was becoming not uncommon. 01:17:09.200 --> 01:17:11.588 align:middle line:84% And we'll see this really literally explode in ways 01:17:11.588 --> 01:17:13.130 align:middle line:84% that matter even to us, when we think 01:17:13.130 --> 01:17:15.470 align:middle line:84% about the history of physics, narrowly, 01:17:15.470 --> 01:17:17.160 align:middle line:90% let alone world history. 01:17:17.160 --> 01:17:20.780 align:middle line:84% It really becomes a tinderbox right around 1900 thereafter. 01:17:20.780 --> 01:17:21.930 align:middle line:90% That's a great question. 01:17:21.930 --> 01:17:23.000 align:middle line:90% Any other questions? 01:17:23.000 --> 01:17:25.600 align:middle line:90% 01:17:25.600 --> 01:17:26.850 align:middle line:90% I'm running a little bit late. 01:17:26.850 --> 01:17:29.680 align:middle line:84% I know some of you might have to run off to a 2:30 class. 01:17:29.680 --> 01:17:30.730 align:middle line:90% So I'll stop there. 01:17:30.730 --> 01:17:32.080 align:middle line:90% Great questions and discussion. 01:17:32.080 --> 01:17:33.960 align:middle line:90% And I'll see you on Wednesday. 01:17:33.960 --> 01:17:34.810 align:middle line:90% And stay tuned. 01:17:34.810 --> 01:17:37.060 align:middle line:84% We'll post the paper 1 assignment real soon. 01:17:37.060 --> 01:17:39.200 align:middle line:90% Stay well, everyone. 01:17:39.200 --> 01:17:55.000 align:middle line:90%