Lecture 1 - How Do You Know?

Overview

Professor McBride outlines the course with its goals and requirements, including the required laboratory course. To the course's prime question "How do you know" he proposes two unacceptable answers (divine and human authority), and two acceptable answers (experiment and logic). He illustrates the fruitfulness of experiment and logic using the rise of science in the seventeenth century. London's Royal Society and the "crucial" experiment on light by Isaac Newton provide examples. In his correspondence with Newton Samuel Pepys, diarist and naval purchasing officer, illustrates the attitudes and habits which are most vital for budding scientists - especially those who would like to succeed in this course. The lecture closes by introducing the underlying goal for the first half of the semester: understanding the Force Law that describes chemical bonds.

Lecture Chapters

Introduction: Logistics
The Goals of Freshman Organic Chemistry: How Do You Know?
Bacon's Instauration: Experimentation over Philosophy
How to Succeed in Chem 125: Following Samuel Pepys
Atoms, Molecules, and Hooke's Law

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Transcript	Audio
html Freshman Organic Chemistry I CHEM 125a - Lecture 1 - How Do You Know? Chapter 1. Introduction: Logistics [00:00:00] Professor Michael McBride: Okay. So for 150 years organic chemistry courses have tended to acquire a daunting reputation. So you need help. I know you're very able, but trust me, you need help. So where do you [get] the help? The PowerPoints are available on the Web. How many of you've already seen the PowerPoint for today, just so I have some idea? So about a quarter of you maybe. Okay, but anyhow, so your lecture notes are important, but you don't have to worry about getting everything down because you can download it from the Web. And I do it on a Mac, but I try my best to make it compatible with PCs and even with the free PC Viewer for PowerPoint. So you should be able to see it. But I don't see it on a PC. So if anything doesn't come through, let me know so that I can fix it. Okay then, in-class discussion is very important, and if you're really, really shy and can't participate in discussion in class, then email me a question. Okay? There's the course website, which is our substitute for a text. It also includes the PowerPoint, and there's the link for it, and when go there you'll see it develop. The current website is mostly last year's course, so it'll change a little bit as we go along, but fundamentally it's the same. If you want to look ahead you'll see pretty much what's coming up. There'll be assigned problems and questions, and also there are previous exams and answers keys. All these things are on the course website so you'll get help there. But one thing that's really special is the course Wiki. This is the third year we've done it and the second year in a really systematic way. So you get assigned to do, to cover a couple frames of the PowerPoint. So those are the ones you really need to take careful notes on, and write them up, and help other people too; that's the nature of a Wiki, as you know. How many of you have participated in a Wiki? Well, by next week it will be all of you. Okay, but in order to get credit for it you have to get it by the night after the lecture. So for the lecture today you have to get it by late tomorrow night, 36 hours after the lecture. This is so other students can use it. Okay, in the spring there'll probably be a textbook. I haven't really decided yet. These things cost an arm and a leg. Maybe we can find one that's used, an older edition. It doesn't make any difference except to the publishers. Okay, also there's personal help, like from me, and there's — and you can find my phone number, email and so on, on the website. Also the two graduate student TAs who are assigned to the course, who are Filip Kolundzic — Filip, back there — and Nathan Schley, not Schlay, Schley. So these are graduate students in chemistry and they run these discussion sections. Typically you have a 50-minute discussion section. But the way we run it in this course is that on two different nights a week there are two-hour sessions. You can come to any part of it you want to. You can go to both of them, you can go to four hours a week if you want to, or you can go to none at all if you want to. So really, for the bookkeeping purposes of the department you have to sign up for a section. Sign up for any section you want to and then come to what's useful for you. But also, the reason you pay the big bucks to come here, is not to hear me, it's to interact with the other students. That's a really big help. So, form study groups. And in fact you can get advice from previous people who've taken the course. That's on the Web. Also there's some of them, there's a list of them on the Web who would be happy to talk to you if you need it. And we're blessed with three alumni, seniors who took this course as freshmen, who act as what are called peer tutors, and they'll run a session Sunday evening, from eight to ten p.m. is the current plan. We'll announce the rooms for these things on the website and probably by email to you as well. So let me introduce Tina Ho and Drew Klein and Justin Kim. So they'll be a big help to you too. So there's plenty of personal help, so use it. These are the dates we're going to have exams. There are ten lectures and then an exam; nine lectures, exam; nine lectures, exam. Actually, if you check, you'll find that — and also you get 50 points for participation in the Wiki, and the total is 650 points, that's what your exam is based on. Actually this doesn't cover — it's nine lectures that are covered on the exam, but the previous Wednesday part of the lecture is going to be a guest lecturer that's going to be here just that day. So we're putting the exam off and it'll only cover the previous material; not that that's a big deal. Okay, and the semester grade is biased; that is, it's based on this, your total score here, out of 650 points. But if you're near a cutoff and you were very good about turning in your problem sets and so on, then we boost you up. We don't grade problem sets but it's worthwhile to do them, and they might make a difference. Chapter 2. The Goals of Freshman Organic Chemistry: How Do You Know? [00:05:36] So where are we going with this? What are the goals of our Freshman Organic Chemistry? In fact, if you click that in your PowerPoint you'll get taken to that site, but it's right on the website, you'll see it anyhow. First is to learn the crucial facts and vocabulary of Organic Chemistry — after all that's what we think we're here for — and to develop a theoretical intuition about how bonding works. This is the goal for, the primary goal of the first half of the fall semester is to learn how bonding works really, and that relates then to molecular structure; and also how bonding changes, and that of course is reactivity. But under the line there are a lot of other things that we do in Freshman Organic Chemistry that are arguably just as important, like make the scientific transition from school to university. In school they try to teach you what people know. In the University you try to develop new knowledge. So you need a different mindset for that, and we hope this course helps you develop that. So learn from Organic Chemistry, which is really in my view a model science, how to be a creative scientist. So here's a creative scientist by anybody's measure, Louis Pasteur. And in the 1880s he said this in French, but in English it says, "Knowing to be astonished by something is the mind's first step toward discovery." Another way of putting that is that the characteristic comment on making a real discovery is not "Eureka", it's "Huh, that's funny." So that's what you really have to learn; learn enough about how chemistry works and form this picture in your mind that when something happens that doesn't fit, you know to be astonished so that you can discover something. That's exactly what Pasteur did, and we'll talk about that in the course. And even perhaps more important, to develop good taste, so that you can distinguish sense from nonsense; there's certainly more nonsense floating around than sense, and being able to tell the difference is important. The way you do it is to develop good taste by looking at a lot of good examples and then you're aware of how crummy the bad examples are. So we're going to try to emphasize good examples, and have fun. So and as we go along, if you have questions, break in. You'll do this much more as we go along, I know. So the class really is mostly about theory, although we describe the basis for the theory and spend a lot of time trying to make it real. But we require Chemistry 126L, the lab. This is the only chemistry course that requires you to take a lab simultaneously. So I hope you're all enrolling in that because there'll be a certain day that you want to be able to take it. It's just one afternoon a week, three hours or whatever it is, but you want to get your first choice, so line up soon. You'll be accommodated but it's just more convenient if you get it arranged earlier. But why? Because lab answers the really big question. And the big question was brought home to me by my son, John McBride, in his third year. This was the beginning of the third year, and his mother and I didn't know what was coming. For the next year, maybe 15, maybe 20 times a day, he said, "How do *you* know?" So here's John this last summer. He's now 38 and he has his own three-year-olds to say that to him. And he doesn't say, "How do *you* know?" anymore. He now says, "How do you *know?" Okay? But that is the main question, how do you know what these things that they told you in school? Well, there are four ways we can talk about of knowing, and two of them are shown on this manuscript from the Carolingian book painter. If we zoom in on the top frame, here's Moses on Mount Sinai. So the first way of knowing is divine authority. Here he's going to be the — here's the graduate student here getting the word. Here's the teaching assistant over on the left perhaps. [Laughter] Aaron, right? And then he comes down from Sinai, to see the class, the Children of Israel. So here's another kind of authority, which is human authority interpreting the scriptures. And here you can see the class; the guys are going like "huh." And the teaching assistant is off on the side still. But this doesn't make it. Science is not faith based. There may be other things you know that way but not science. Science ignores divine authority and it ignores human authority; not that they might not exist but they don't relate to science. Now as you walked in today, did you notice these things over here? There's an Honor Roll of Chemists, and in fact we'll use that a lot this semester, and in particular one of the people on there is Michael Faraday, who started in a very humble way. He was a book binder's apprentice and he bound this book — not this particular copy but this book — which is called Conversations on Chemistry. He bound the first edition. This one is a later edition. So you see it's Conversations on Chemistry in which Elements of that Science are Familiarly Explained and Illustrated by Experiments. And who's the author? J. L. Comstock; he's actually not the author, he's the guy who stole it. He stole it from a woman, Mrs. Marcet, in England, who wrote this book, which was the most popular textbook — it was written for girls — but it was the most popular textbook in all chemistry, for the first half of the nineteenth century. It went through like 20-some editions. And here you see at the beginning it's a dialogue, a conversation between Mrs. B and Caroline and Emily, and it's fun to see this here, what Emily says at the beginning. "To confess the truth Mrs. B, I'm not disposed to form a very favorable idea of chemistry, nor do I expect to derive much entertainment from it." But in the long run, as you can imagine, they have a lot of fun with chemistry. It was a wonderful book, and still is. But he was binding it, and read it. And look what he says about this, as his introduction to be the leading experimental scientist of the nineteenth century: "Do not suppose I was a very deep thinker or was marked as a precocious person. I was a very lively, imaginative person and could believe in the Arabian Knights as easily as the encyclopedia, but facts were important to me and saved me. I could trust a fact and always cross-examined an assertion. So when I questioned Mrs. Marcet's book by such little experiments as I could find means to perform, and found it true to the facts, as I could understand them, I felt I had got hold of an anchor in chemical knowledge and clung fast to it." So the experiments were what did it. So the third way of knowing is by experimental observation. And here's Richard Feynman. How many of you've heard of Richard Feynman? He was a really great physicist, wrote a wonderful textbook as well as getting all sorts of prizes. He spoke to the National Science Teachers Association in 1966 saying, "Learn from science that you must doubt the experts. Science is the belief in the ignorance of experts. When someone says, 'Science teaches such and such,' he's using the word incorrectly. Science doesn't teach it; experience teaches it. If they say to you, 'Science has shown such and such,' you might ask, 'How does science show it? How did the scientists find out? How, what, where?' Not science has shown, but this experiment or this effect has shown." Now, why do we quote Feynman? Because he's an expert. [Laughter] Wrong. Though literally, expert, the etymology of expert, is it means someone who has done experiments. We quote him because what he says makes sense. So logic is the fourth way of knowing things. So the two ways that we know things in chemistry, or in science, are experiment and logic. And the lecture is a little bit more focused on logic and the lab is more focused on experiment, and you get an unbalanced view if you do one without the other. Chapter 3. Bacon's Instauration: Experimentation over Philosophy [00:15:17] Okay, so modern science got underway in the seventeenth century. There's the seventeenth century, 1600 to 1700. And 1638 was when New Haven Colony was founded, and 1701 was when Yale was founded. So that's when everything got underway, just when this enterprise was beginning here. Here we are. If you go back 100 years you get to quantum, quantization by Planck; and we'll talk about that. And if you go back another 100 years you get to Lavoisier and oxidation; and we'll talk about that. And if you get another 100 years you get to Newton and gravitation; and we'll talk a little bit about that. And if you go back a little more, another 100 years, you get to Copernicus and the revolution of the heavenly bodies, and Columbus and navigation, and Luther and the Reformation. And these things all have something in common. As Robert Hooke wrote, "The seventeenth century" (his age) "was an age, of all others, the most inquisitive." All these things have to do with people inquiring into how people know things and finding out new things. And in particular an important figure was Francis Bacon and his Instauration. Now you may not know The Instauration* so well, let's look at that. Here's Francis Bacon, there are his years. He was Elizabethan and Jacobean. He was almost exactly contemporary with Shakespeare, and with Galileo. He went to school, to university, at Cambridge. And here's a cartoon that shows him — it's a modern cartoon — imagining him in a class at Cambridge. Because he wrote of his tutors at Cambridge: "They were men of sharp wits, shut up in their cells of a few authors, chiefly Aristotle, their dictator. All the philosophy of nature" (philosophy meant science in those days) "all the philosophy of nature, which is now received, is either the philosophy of the Grecians or that of the alchemists. The one is gathered out of a few vulgar" (that means 'common' of course) "observations, and the other out of a few experiments of a furnace. The one never faileth to multiply words, and the other ever faileth to multiply gold." So here's the book he wrote, The Instauration. That's the frontispiece for it. This picture's from the Beinecke Library; I went down and got a picture of the book. Notice it was published in 1620. What else happened then? That's when the Pilgrims came over, right? So the title of the book, rather small under his name and title as Lord Chancellor of England, is Instauratio Magna, which means the Great Restoration. Restoration of what? Of the way of knowing. A bigger, a part of it, it's called the Novum Organum, which is — and it develops the inductive scientific method, based on experiment, to replace Aristotelian deduction, which is you maybe did one experiment sometime, and then you reason everything from that. But he says no, you have to do more experiments. Now there's an interesting thing here. One of the devices on the title, on this frontispiece, is two pillars. What in the world are they doing there? Well they're the same pillars that you see on this. That's a piece of eight; you know, Treasure Island, pieces of eight? See it's eight reales, and it came from the silver of Mexico; it was minted in Mexico City. So and there you see the same pillars and on them it says plus ultra; more beyond. Beyond what? What are the pillars? Pardon me? Student: Spain and Africa. Professor Michael McBride: Yes, it's Africa and Spain, but it's the Pillars of Hercules, which are the mouth of the Mediterranean, the old Classical World. So there's the Mountain of Moses in Morocco and the Mountain of Tarik, which is the name of Gibraltar. So here's the Mediterranean, the Classical World of Aristotle, and you can sail out into the New World and bring back silver, for example. There's danger of course. But look at what it says at the bottom. What will be brought back? Not just silver. Multi pertransibunt & augebitur scientia — "Many will pass through and knowledge will be increased." So we go beyond Aristotle into experimentally based science and knowledge will be increased. So here's some quotes from The Instauratio Magna. "That wisdom which we have derived principally from the Greeks" (no offense, okay?) "is but like the boyhood of knowledge, and has the characteristic property of boys: it can talk but it cannot generate;" "…it is but a device for exempting ignorance from ignominy." That means it's a way of hiding your ignorance, and we'll see examples of that. We'll talk about, in Lecture 11, about correlation energy, and we'll talk in Lecture 32 about strain energy, and you'll see that both of these are just words that are used to hide our ignorance. "…the end which this science of mine proposes is the invention, not of arguments, but of arts" (ways of doing things). "…not so much by instruments" (although new instruments are important, like microscopes and so on) "as by experiments, skillfully and artificially devised for the express purpose of determining the point in question." (So artificial experiments designed to decide a question; experiments.) "And this will lead to the restoration of learning and knowledge." So followers of Bacon established The Royal Society in 1662, just after Charles was restored to England, after the period of Cromwell. And there was a history written of The Royal Society, a book about this thick, published in 1667, only five years after it was founded. Why did they publish a history so soon? Well let's look at this, the frontis itpiece of this book. Here's the late Francis Bacon, who was said to be Artium Instaurator, the Restorer of the Arts. And here's the President of The Royal Society, the mathematician, Viscount Brouncker, and here in the middle, being crowned with laurel, is Charles II. Why do they have him up on a pedestal? Because they're hoping, as scientists have before and ever since, to extract some money out of the government to do their research. They actually never got it from Charles but it wasn't for lack of trying. And this is why they wrote the history, to try to make the case for being supported. Okay, now let's look at all the good things that will come from science, from The Royal Society. In the background can you see what that is? We'll blow it up. Here there's a hint to it on the bookshelf. If you look really fine on the bookshelf you can see that some of them have writing on the spine. Do you see what that one is? Can anybody read it? What? What science book do you think they might have had? Student: Copernicus. Professor Michael McBride: Copernicus, right? So astronomy; that's a telescope in the back. Okay, or over here on the wall, what's that thing? It's a clock. Why is it shaped like a piece of pie? Student: Because it has a pendulum inside. Professor Michael McBride: Ah, because it has a pendulum inside. So horology, making good clocks. Okay, or here, what's that thing? It's hard for you to know. Student: Solar. Professor Michael McBride: It's a wind gauge. It has a vane inside that it blows on — and you can tell from how far it goes on the scale how strong the wind is. So meteorology. And back here on the pillar, what are those things for? Students: A compass. Professor Michael McBride: For cartography. Now what do all these things have in common that they're going to do for Charles II? Astronomy — Student: For the records. Professor Michael McBride: Good clocks, meteorology, cartography, what — [Students speak over one another] Professor Michael McBride: They all have to do with navigation, with making England strong at sea. Now back here is another science, Chemistry. That doesn't seem to have anything to do with navigation. Why would Chemistry be important to Charles? Student: War. Professor Michael McBride: Look at it. Student: War. Professor Michael McBride: To make gun powder. There was a chapter about gun powder in The History of the Royal Society. Okay, and up here at the top is the motto, which is Nullius in Verba, which comes from this quote from Horace, and what it says is, "Lest you ask who leads me, in what household I lodge" (that is, what philosophy I advocate) "there is no master in whose words I am bound to take an oath. Wherever the storm forces me, there I put in as a guest." So it's the experiment, not the philosopher, that leads you to the conclusion. So Nullius in Verba is 'in the words of none.' And, in fact, the original name of The Royal Society was The Royal Society for the Improving of Natural Knowledge by Experiments. Okay, so we're going to see, as the course goes along, important experiments that really decided questions, and in fact Bacon's most important kind of experiment was one that "finally decides between two rival hypotheses, proving the one and disproving the other." So you can do all sorts of experiments and just be collecting butterflies — no, I don't mean to insult people who collect butterflies, it's a fine thing to do. But there's something special about experiments that really are designed to answer a question. Now Bacon devised a name for such experiments, and they're based on this model, that you have a road that diverges and you need to know which way to go between these two hypotheses. What do you need, to know which way to go? You need a sign, or this was a cross that you mounted at a crossroads. So the Latin name for cross is crux. Do you see what they call the experiment? Crucial. That's the origin of the word crucial, right? It's the one that tells you which way to go. Okay, so here is Isaac Newton and he's holding something. Can you see what he's holding in his hand? Student: A candle. Professor Michael McBride: I'll give you a hint. It's a prism. Why is he holding a prism? Because that was his crucial experiment; and here's his diagram in that experiment with a prism in it. He called it the Experimentum Crucis, taking the word from Bacon. Okay, so light came in through a hole in the window, through a lens, and then got bent and dispersed into the different colors. So you get a spectrum here on this thing, the different colors. Now there's the question, how does the prism make color? Hooke and Descartes thought that light was a train of pulses and as it goes through something like a prism, or as it reflects from a thin layer of oil on water or something like that, that it changes the timing of the pulses and therefore changes the color. But Newton thought that the colors were pre-existing, and the prism just separates them. And this was his crucial experiment to decide between those two theories. You see what he did? He drilled a hole through the board and let through only the red light, and put a second prism there. And he wrote here, three times — he wrote it here, and also here, and also here — nec variat lux fracta colorem; which means "the broken light does not change its color." So this proved to Newton, at least at that time, that light is a substance, not a train of pulses. What do you think of that proof now? You think light is a substance or a train of pulses? Students: Both. Student: Neither. Professor Michael McBride: But at least you can see that in terms then, that was a crucial experiment, a really important experiment, and that's the kind of experiments we'll try to talk about in the course. Experiments are indispensable in Organic Chemistry. It's an empirical science based on observation, and that's why you have to take the lab. But so is logic — that was number three and number four of the ways of knowing — logic is important too. So believe what I tell you here only when it makes sense to you. Don't just cram it in, make sure it makes sense. But what if it doesn't? Chapter 4. How to Succeed in Chem 125: Following Samuel Pepys [00:30:15] Now here's how to succeed in Chem. 125, and we'll take as our model science student Samuel Pepys. How many people have heard of Samuel Pepys? Have you heard of him as a scientist? Student: I don't remember. Professor Michael McBride: What did you hear of him as? What do you associate with Samuel Pepys? Student: Newton-Pepys Problems. Professor Michael McBride: Right in this period, in the heart of the science growth. But what you know him for was his diary, which tells all about life, everyday life in Restoration London. He was actually, as a sixteen-year-old, present when Charles I was beheaded in 1649. Now what's the connection? Do you know where this is? Anybody been there? Dixwell, Goffe and Whalley Avenues, those are named for three of the 50 judges that condemned Charles I to be beheaded, and they were the only ones that lasted very long, after the Restoration, and they lasted because they fled to New England and were hidden on West Rock. All these roads are heading west toward West Rock. Okay, so that's a tie-in to the same period. But anyway, he got his B.A. in Cambridge in 1654 and a Master's in 1656. And he got a good job, he became Clerk of the Acts for the Navy Board, which meant he was the guy that purchased everything for the Royal Navy, all the rope, all the tar, all the lumber and so on. And on July Fourth, 1662 — it's the fourth of July but it's more than 100 years before that became relevant — he writes in his diary, "By and by comes Mr. Cooper, mate of the Royall Charles, of whom I intend to learn mathematiques, and do begin with him to-day, he being a very able man… After an hour's being with him at arithmetique (my first attempt being to learn the multiplication-table); we then parted till tomorrow." So here was the guy doing all the purchasing for the Royal Navy and he didn't know multiplication, let alone division. But he worked hard at it. July ninth, five days later: He's "Up by four o'clock, and at my multiplicacion-table hard, which is all the trouble I meet withal in arithmetique." He can do the other things pretty well. July eleven: "Up by four o'clock and hard at my multiplicacion-table, which I am now almost master of." Christmas — so six months later: "…so to my office, practicing arithmetique alone and making an end of last night's book with great content till eleven at night and so home to supper and to bed." Or a year later — so he was motivated and he was diligent; that's good. A year later, on a Sunday: "…I below by myself looking over my arithmetique books and timber rule. So my wife arose anon and she and I all the afternoon at arithmetique," [laughter] "and she has come to do Addition, Subtraction and Multiplicacion very well, and so I purpose not to trouble her yet with Division…" Right? [Laughter] So he worked with a study partner, and that's crucial. And Isaac Newton — does anybody recognize this book? Student: Yes, sure. Professor Michael McBride: Right? The Mathematical Principles of Science, of Natural Philosophy. But there's an interesting thing on the title page. Samuel Pepys is the one who gave permission to publish that book, because he was the president of The Royal Society. Now six years later Pepys encountered a problem with dice. The reason was he went to coffee shops every night for dinner and they'd gamble, and people proposed various kinds of bets, and he couldn't figure out this one, so he wrote Newton for help. So this was the problem that he wrote to Newton, twenty-second of November. So A has six dice in a box, and he has to throw a Six by throwing it; B has 12 dice and he has to fling two Sixes; and C has 18 Dice but he has to get 3 Sixes to win. The question, "Whether B and C have not as easy a Taske at A, at even luck?" That is, if the dice aren't loaded or anything, who has the better bet? [Laughter] How many people think that it's the same? Don't be shy. How many think it's A? How many think B? How many think C? How many don't really have any opinion at all? Good, that wins. Okay, so he wrote this letter to try to get help on his bets from Newton, and Newton replied, four days later, "What is the expectation or hope of A to throw every time one six, at least, with six dyes?" So you get two sixes you still win; that wasn't clear in the original statement. So he says, "If we formulate the question that way, it appears by an easy computation that the expectation of A is greater than B or C; that is, the task of A is the easiest." There's the answer. So Pepys replied on the sixth of December: "You give it in favour of the Expectations of A, & this (as you say) by an easy Computation. But yet I must not pretend to soe much Conversation with Numbers, as presently to comprehend as I ought to doe, all the force of that wch you are pleas'd to assigne for the Reason of it, relating to their having or not having the Benefit of all their Chances." So he wasn't ashamed to admit that he didn't really understand — that's crucial. "And therefore, were it not for the trouble it must have cost you, I could have wished for a sight of the very Computation. " Can you show me how to figure it out? And he wanted that because somebody might change the terms of the bet and then he wouldn't know. He wanted really to understand. He insisted on proof. So this is two of the pages from Newton's correspondence of the letter that he wrote in response, and you can see that Pepys certainly got more than he had bargained for. "So to compute this I set down the following progressions of numbers." So you can go through all this and you get complicated quotients here, and it turns out that A has 31,031 chances out of 46,656, or 0.6651 chance of winning, and B has this, which is 0.6187; A wins. So is Pepys satisfied with this? Pepys writes back and he says, "Why?" Right? "I cannot bear the Thought of being made Master of a Jewell I know not how to wear." So he's willing to swallow his pride to search for really solid understanding. Now compare this with a comment we got at an end-of-semester evaluation in January a year ago. "I never went to his office hours for help because I felt like he would make me feel stupid, because he's superior to me in chemistry." I hope I'm superior to you in chemistry. [Laughter] I'm not superior as a person, but I hope I'm superior in chemistry. You're paying me the big bucks because of that. So swallow your pride and ask someone for help. Follow Pepys. So read "Pepys and Newton" and get together to do problems for Monday, and contribute to the Wiki when you're asked to do so. So here are problems. For Friday the problems are optional but very helpful. One is find out which two class members have the rooms nearest you so that you can maybe use them as study partners. You don't have to use them, use anybody, but use someone, don't try to go it alone. Two. What are the three most common items of advice from course veterans? So if you click there, or go to the webpage, you can get anonymous advice; I was careful to make sure it's anonymous. So you can get all — much of it is contradictory, so your job is to look through it and try to get some idea of what they're telling you that's worth knowing. For Monday there are problems from that webpage, "Pepys & Newton." And let me tell you that you better get together with other people to do it, because there's a lot of stuff there. So get together in a group, parcel out who works on what, discuss what went on and so on. And then for a week from Friday there's stuff about drawing Lewis Structures, from another webpage about functional groups. So we'll get to that later, I just wanted you to know what's coming up. Incidentally, this thing about the problems set that has to do with the mathematics that Newton and Pepys were working on there, has to do with isotope ratios. You know, chlorine has a funny atomic weight. Why? What is the atomic weight, does anybody know? Student: 35.5. Professor Michael McBride: Thirty-five and a half. Why a half? Most of the elements are pretty near integers. It's because it's a mixture of isotopes. It's a quarter of one isotope and three-quarters of the other, and the average is thirty-five and a half; thirty-five and thirty-seven. But in fact it depends on where you get chlorine from, what the ratio is. There's thirty-five and a half for a standard atomic weight, but it ranges quite a bit, depending on where you get it. So by measuring these ratios, which is a lot like these odds in the betting, you can tell where things came from. You can tell where hydrocarbons came from sometimes that way. And those are the problems that you have to deal with. So it's not really very, very relevant to the course as a whole, but it's relevant to the Pepys and Newton thing and it's a fun problem. So that's what you've got to do for Monday. Okay, and here are the assignments. I emailed all these people. I hope you're here, and that you picked up on what we talked about today so that you can improve the Wikis from last year. Last year people developed their Wikis from scratch. This time — which is a very valuable thing to do. So I was torn this year as to whether to have you do them from scratch or whether to modify last year. I figured modifying last year is better because then you have something to read earlier on, for those who are not working on developing it. So anyhow, but the hope is — so if you modify it — it has to be something significant, not put a comma in or something like that, but add something useful to understanding. If you do it within thirty-six hours, you get two points, and if what you do is really good, you get three points. So you go to that page and you click on those things and then you can read what — or you can either modify them or read it; it's a Wiki. Chapter 5. Atoms, Molecules, and Hooke's Law [00:41:56] Now, we come to the question that we'll address more. We have another five minutes here. The question we're really dealing with now, having seen how to work in Chem. 125, is are there atoms and molecules; how do you know? And what force holds them together? Because if we knew that they're real, and we knew what force held them together, then in principle we might be able to calculate everything. So it would all be theory. So is it springs that hold atoms together? So Robert Boyle — notice he's right at that time, 1627 to 1691, and he's the oldest person that's on the Honor Roll outside the building here, he's over that way — so Robert Boyle wrote this first important book in chemistry, New Experiments Physico-Mechanical: Touching the Spring of Air. So you know Boyle's Law, how pressure and volume change, that air in a piston acts like a spring. So PV is a constant; that's Boyle's Law. So he developed this science on the basis of a new instrument, the pneumatical engine, which was built by Robert Hooke, the guy we quoted. And there's a picture of the air pump here with that crank on it, and so on to pump things in or out of that bulb. Now a couple of years later Hooke wrote this book, Lectures, De Potentia Restitutiva, or of Spring, explaining the power of springing bodies. And this is the beginning of that book. "The Theory of Springs, though attempted by divers eminent Mathematicians of this Age has hitherto not been Published by any. It is now about eighteen years since I first found it out, but designing to apply it to some particular use, I omitted the publishing thereof." So he kept it secret so no one would steal the idea. What did he hope to do with a spring, a really important technology that he could do with a spring? There was a coil in the spring that he depended on. Student: Flying. Student: Pendulum clock. Professor Michael McBride: A new kind of clock, one that could work better for navigation. It was his spring that actually allowed Harrison, 100 years later, to win the contest about making an accurate clock; some of you must know that story. So anyhow he had been hiding this so it wouldn't be stolen. In fact, it was stolen by Huygens. So "about three years since His Majesty was pleased to see the experiment that made out this theory, tried at White Hall, and also my spring watch. About two years since I printed the theory in an anagram at the end of my book on the description of helioscopes, viz." this. So this is what he published at the end of this book on helioscopes, and that is an anagram of how springs work, so that later he could prove that he knew it, if needs be, but no one could steal it in the meantime. And if you unscramble it, it's "Ut tensio sic vis; that is, the power of any spring is in the same proportion with the tension thereof. That is, if one power stretch or bend at one space, two will stress at two, three will bend at three, and so forward." So here's his figure that shows that. That's Hooke's Law, the force law. The force is proportional to the distortion. So here's his figure, and he's got plots of it here. Ut tensio (as the extension) sic vis (so the force). So it's linear, the force is how much you stretch it. And he has lots of different kinds of springs that do that. Here's this clock kind of spring, a coil spring, just stretching a wire. So the force is proportional to the extension. Or another way of saying it is, "The potential energy is proportional to the square of the extension." So it's a parabola. So that's Hooke's Law, and that's where we'll take up next time. [end of transcript] Back to Top	mp3

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Freshman Organic Chemistry I

CHEM 125a - Lecture 1 - How Do You Know?

Chapter 1. Introduction: Logistics [00:00:00]

Professor Michael McBride: Okay. So for 150 years organic chemistry courses have tended to acquire a daunting reputation. So you need help. I know you're very able, but trust me, you need help. So where do you [get] the help? The PowerPoints are available on the Web. How many of you've already seen the PowerPoint for today, just so I have some idea? So about a quarter of you maybe. Okay, but anyhow, so your lecture notes are important, but you don't have to worry about getting everything down because you can download it from the Web. And I do it on a Mac, but I try my best to make it compatible with PCs and even with the free PC Viewer for PowerPoint. So you should be able to see it. But I don't see it on a PC. So if anything doesn't come through, let me know so that I can fix it. Okay then, in-class discussion is very important, and if you're really, really shy and can't participate in discussion in class, then email me a question. Okay?

There's the course website, which is our substitute for a text. It also includes the PowerPoint, and there's the link for it, and when go there you'll see it develop. The current website is mostly last year's course, so it'll change a little bit as we go along, but fundamentally it's the same. If you want to look ahead you'll see pretty much what's coming up. There'll be assigned problems and questions, and also there are previous exams and answers keys. All these things are on the course website so you'll get help there. But one thing that's really special is the course Wiki. This is the third year we've done it and the second year in a really systematic way. So you get assigned to do, to cover a couple frames of the PowerPoint. So those are the ones you really need to take careful notes on, and write them up, and help other people too; that's the nature of a Wiki, as you know. How many of you have participated in a Wiki? Well, by next week it will be all of you. Okay, but in order to get credit for it you have to get it by the night after the lecture. So for the lecture today you have to get it by late tomorrow night, 36 hours after the lecture. This is so other students can use it. Okay, in the spring there'll probably be a textbook. I haven't really decided yet. These things cost an arm and a leg. Maybe we can find one that's used, an older edition. It doesn't make any difference except to the publishers.

Okay, also there's personal help, like from me, and there's — and you can find my phone number, email and so on, on the website. Also the two graduate student TAs who are assigned to the course, who are Filip Kolundzic — Filip, back there — and Nathan Schley, not Schlay, Schley. So these are graduate students in chemistry and they run these discussion sections. Typically you have a 50-minute discussion section. But the way we run it in this course is that on two different nights a week there are two-hour sessions. You can come to any part of it you want to. You can go to both of them, you can go to four hours a week if you want to, or you can go to none at all if you want to. So really, for the bookkeeping purposes of the department you have to sign up for a section. Sign up for any section you want to and then come to what's useful for you. But also, the reason you pay the big bucks to come here, is not to hear me, it's to interact with the other students. That's a really big help. So, form study groups. And in fact you can get advice from previous people who've taken the course. That's on the Web. Also there's some of them, there's a list of them on the Web who would be happy to talk to you if you need it.

And we're blessed with three alumni, seniors who took this course as freshmen, who act as what are called peer tutors, and they'll run a session Sunday evening, from eight to ten p.m. is the current plan. We'll announce the rooms for these things on the website and probably by email to you as well. So let me introduce Tina Ho and Drew Klein and Justin Kim. So they'll be a big help to you too. So there's plenty of personal help, so use it.

These are the dates we're going to have exams. There are ten lectures and then an exam; nine lectures, exam; nine lectures, exam. Actually, if you check, you'll find that — and also you get 50 points for participation in the Wiki, and the total is 650 points, that's what your exam is based on. Actually this doesn't cover — it's nine lectures that are covered on the exam, but the previous Wednesday part of the lecture is going to be a guest lecturer that's going to be here just that day. So we're putting the exam off and it'll only cover the previous material; not that that's a big deal. Okay, and the semester grade is biased; that is, it's based on this, your total score here, out of 650 points. But if you're near a cutoff and you were very good about turning in your problem sets and so on, then we boost you up. We don't grade problem sets but it's worthwhile to do them, and they might make a difference.

Chapter 2. The Goals of Freshman Organic Chemistry: How Do You Know? [00:05:36]

So where are we going with this? What are the goals of our Freshman Organic Chemistry? In fact, if you click that in your PowerPoint you'll get taken to that site, but it's right on the website, you'll see it anyhow. First is to learn the crucial facts and vocabulary of Organic Chemistry — after all that's what we think we're here for — and to develop a theoretical intuition about how bonding works. This is the goal for, the primary goal of the first half of the fall semester is to learn how bonding works really, and that relates then to molecular structure; and also how bonding changes, and that of course is reactivity. But under the line there are a lot of other things that we do in Freshman Organic Chemistry that are arguably just as important, like make the scientific transition from school to university. In school they try to teach you what people know. In the University you try to develop new knowledge. So you need a different mindset for that, and we hope this course helps you develop that. So learn from Organic Chemistry, which is really in my view a model science, how to be a creative scientist.

So here's a creative scientist by anybody's measure, Louis Pasteur. And in the 1880s he said this in French, but in English it says, "Knowing to be astonished by something is the mind's first step toward discovery." Another way of putting that is that the characteristic comment on making a real discovery is not "Eureka", it's "Huh, that's funny." So that's what you really have to learn; learn enough about how chemistry works and form this picture in your mind that when something happens that doesn't fit, you know to be astonished so that you can discover something. That's exactly what Pasteur did, and we'll talk about that in the course. And even perhaps more important, to develop good taste, so that you can distinguish sense from nonsense; there's certainly more nonsense floating around than sense, and being able to tell the difference is important. The way you do it is to develop good taste by looking at a lot of good examples and then you're aware of how crummy the bad examples are. So we're going to try to emphasize good examples, and have fun. So and as we go along, if you have questions, break in. You'll do this much more as we go along, I know.

So the class really is mostly about theory, although we describe the basis for the theory and spend a lot of time trying to make it real. But we require Chemistry 126L, the lab. This is the only chemistry course that requires you to take a lab simultaneously. So I hope you're all enrolling in that because there'll be a certain day that you want to be able to take it. It's just one afternoon a week, three hours or whatever it is, but you want to get your first choice, so line up soon. You'll be accommodated but it's just more convenient if you get it arranged earlier.

But why? Because lab answers the really big question. And the big question was brought home to me by my son, John McBride, in his third year. This was the beginning of the third year, and his mother and I didn't know what was coming. For the next year, maybe 15, maybe 20 times a day, he said, "How do you know?" So here's John this last summer. He's now 38 and he has his own three-year-olds to say that to him. And he doesn't say, "How do you know?" anymore. He now says, "How do you know?" Okay? But that is the main question, how do you know what these things that they told you in school?

Well, there are four ways we can talk about of knowing, and two of them are shown on this manuscript from the Carolingian book painter. If we zoom in on the top frame, here's Moses on Mount Sinai. So the first way of knowing is divine authority. Here he's going to be the — here's the graduate student here getting the word. Here's the teaching assistant over on the left perhaps. [Laughter] Aaron, right? And then he comes down from Sinai, to see the class, the Children of Israel. So here's another kind of authority, which is human authority interpreting the scriptures. And here you can see the class; the guys are going like "huh." And the teaching assistant is off on the side still. But this doesn't make it. Science is not faith based. There may be other things you know that way but not science. Science ignores divine authority and it ignores human authority; not that they might not exist but they don't relate to science.

Now as you walked in today, did you notice these things over here? There's an Honor Roll of Chemists, and in fact we'll use that a lot this semester, and in particular one of the people on there is Michael Faraday, who started in a very humble way. He was a book binder's apprentice and he bound this book — not this particular copy but this book — which is called Conversations on Chemistry. He bound the first edition. This one is a later edition. So you see it's Conversations on Chemistry in which Elements of that Science are Familiarly Explained and Illustrated by Experiments. And who's the author? J. L. Comstock; he's actually not the author, he's the guy who stole it. He stole it from a woman, Mrs. Marcet, in England, who wrote this book, which was the most popular textbook — it was written for girls — but it was the most popular textbook in all chemistry, for the first half of the nineteenth century. It went through like 20-some editions. And here you see at the beginning it's a dialogue, a conversation between Mrs. B and Caroline and Emily, and it's fun to see this here, what Emily says at the beginning. "To confess the truth Mrs. B, I'm not disposed to form a very favorable idea of chemistry, nor do I expect to derive much entertainment from it." But in the long run, as you can imagine, they have a lot of fun with chemistry. It was a wonderful book, and still is. But he was binding it, and read it. And look what he says about this, as his introduction to be the leading experimental scientist of the nineteenth century:

"Do not suppose I was a very deep thinker or was marked as a precocious person. I was a very lively, imaginative person and could believe in the Arabian Knights as easily as the encyclopedia, but facts were important to me and saved me. I could trust a fact and always cross-examined an assertion. So when I questioned Mrs. Marcet's book by such little experiments as I could find means to perform, and found it true to the facts, as I could understand them, I felt I had got hold of an anchor in chemical knowledge and clung fast to it."

So the experiments were what did it. So the third way of knowing is by experimental observation. And here's Richard Feynman. How many of you've heard of Richard Feynman? He was a really great physicist, wrote a wonderful textbook as well as getting all sorts of prizes. He spoke to the National Science Teachers Association in 1966 saying,

"Learn from science that you must doubt the experts. Science is the belief in the ignorance of experts. When someone says, 'Science teaches such and such,' he's using the word incorrectly. Science doesn't teach it; experience teaches it. If they say to you, 'Science has shown such and such,' you might ask, 'How does science show it? How did the scientists find out? How, what, where?' Not science has shown, but this experiment or this effect has shown."

Now, why do we quote Feynman? Because he's an expert. [Laughter] Wrong. Though literally, expert, the etymology of expert, is it means someone who has done experiments. We quote him because what he says makes sense. So logic is the fourth way of knowing things. So the two ways that we know things in chemistry, or in science, are experiment and logic. And the lecture is a little bit more focused on logic and the lab is more focused on experiment, and you get an unbalanced view if you do one without the other.

Chapter 3. Bacon's Instauration: Experimentation over Philosophy [00:15:17]

Okay, so modern science got underway in the seventeenth century. There's the seventeenth century, 1600 to 1700. And 1638 was when New Haven Colony was founded, and 1701 was when Yale was founded. So that's when everything got underway, just when this enterprise was beginning here. Here we are. If you go back 100 years you get to quantum, quantization by Planck; and we'll talk about that. And if you go back another 100 years you get to Lavoisier and oxidation; and we'll talk about that. And if you get another 100 years you get to Newton and gravitation; and we'll talk a little bit about that. And if you go back a little more, another 100 years, you get to Copernicus and the revolution of the heavenly bodies, and Columbus and navigation, and Luther and the Reformation. And these things all have something in common. As Robert Hooke wrote, "The seventeenth century" (his age) "was an age, of all others, the most inquisitive."

All these things have to do with people inquiring into how people know things and finding out new things. And in particular an important figure was Francis Bacon and his Instauration. Now you may not know The Instauration so well, let's look at that. Here's Francis Bacon, there are his years. He was Elizabethan and Jacobean. He was almost exactly contemporary with Shakespeare, and with Galileo. He went to school, to university, at Cambridge. And here's a cartoon that shows him — it's a modern cartoon — imagining him in a class at Cambridge. Because he wrote of his tutors at Cambridge:

"They were men of sharp wits, shut up in their cells of a few authors, chiefly Aristotle, their dictator. All the philosophy of nature" (philosophy meant science in those days) "all the philosophy of nature, which is now received, is either the philosophy of the Grecians or that of the alchemists. The one is gathered out of a few vulgar" (that means 'common' of course) "observations, and the other out of a few experiments of a furnace. The one never faileth to multiply words, and the other ever faileth to multiply gold."

So here's the book he wrote, The Instauration. That's the frontispiece for it. This picture's from the Beinecke Library; I went down and got a picture of the book. Notice it was published in 1620. What else happened then? That's when the Pilgrims came over, right? So the title of the book, rather small under his name and title as Lord Chancellor of England, is Instauratio Magna, which means the Great Restoration. Restoration of what? Of the way of knowing. A bigger, a part of it, it's called the Novum Organum, which is — and it develops the inductive scientific method, based on experiment, to replace Aristotelian deduction, which is you maybe did one experiment sometime, and then you reason everything from that. But he says no, you have to do more experiments. Now there's an interesting thing here. One of the devices on the title, on this frontispiece, is two pillars. What in the world are they doing there? Well they're the same pillars that you see on this. That's a piece of eight; you know, Treasure Island, pieces of eight? See it's eight reales, and it came from the silver of Mexico; it was minted in Mexico City. So and there you see the same pillars and on them it says plus ultra; more beyond. Beyond what? What are the pillars? Pardon me?

Student: Spain and Africa.

Professor Michael McBride: Yes, it's Africa and Spain, but it's the Pillars of Hercules, which are the mouth of the Mediterranean, the old Classical World. So there's the Mountain of Moses in Morocco and the Mountain of Tarik, which is the name of Gibraltar. So here's the Mediterranean, the Classical World of Aristotle, and you can sail out into the New World and bring back silver, for example. There's danger of course. But look at what it says at the bottom. What will be brought back? Not just silver. Multi pertransibunt & augebitur scientia — "Many will pass through and knowledge will be increased." So we go beyond Aristotle into experimentally based science and knowledge will be increased.

So here's some quotes from The Instauratio Magna. "That wisdom which we have derived principally from the Greeks" (no offense, okay?) "is but like the boyhood of knowledge, and has the characteristic property of boys: it can talk but it cannot generate;" "…it is but a device for exempting ignorance from ignominy." That means it's a way of hiding your ignorance, and we'll see examples of that. We'll talk about, in Lecture 11, about correlation energy, and we'll talk in Lecture 32 about strain energy, and you'll see that both of these are just words that are used to hide our ignorance. "…the end which this science of mine proposes is the invention, not of arguments, but of arts" (ways of doing things). "…not so much by instruments" (although new instruments are important, like microscopes and so on) "as by experiments, skillfully and artificially devised for the express purpose of determining the point in question." (So artificial experiments designed to decide a question; experiments.) "And this will lead to the restoration of learning and knowledge."

So followers of Bacon established The Royal Society in 1662, just after Charles was restored to England, after the period of Cromwell. And there was a history written of The Royal Society, a book about this thick, published in 1667, only five years after it was founded. Why did they publish a history so soon? Well let's look at this, the frontis itpiece of this book. Here's the late Francis Bacon, who was said to be Artium Instaurator, the Restorer of the Arts. And here's the President of The Royal Society, the mathematician, Viscount Brouncker, and here in the middle, being crowned with laurel, is Charles II. Why do they have him up on a pedestal? Because they're hoping, as scientists have before and ever since, to extract some money out of the government to do their research. They actually never got it from Charles but it wasn't for lack of trying. And this is why they wrote the history, to try to make the case for being supported.

Okay, now let's look at all the good things that will come from science, from The Royal Society. In the background can you see what that is? We'll blow it up. Here there's a hint to it on the bookshelf. If you look really fine on the bookshelf you can see that some of them have writing on the spine. Do you see what that one is? Can anybody read it? What? What science book do you think they might have had?

Student: Copernicus.

Professor Michael McBride: Copernicus, right? So astronomy; that's a telescope in the back. Okay, or over here on the wall, what's that thing? It's a clock. Why is it shaped like a piece of pie?

Student: Because it has a pendulum inside.

Professor Michael McBride: Ah, because it has a pendulum inside. So horology, making good clocks. Okay, or here, what's that thing? It's hard for you to know.

Student: Solar.

Professor Michael McBride: It's a wind gauge. It has a vane inside that it blows on — and you can tell from how far it goes on the scale how strong the wind is. So meteorology. And back here on the pillar, what are those things for?

Students: A compass.

Professor Michael McBride: For cartography. Now what do all these things have in common that they're going to do for Charles II? Astronomy —

Student: For the records.

Professor Michael McBride: Good clocks, meteorology, cartography, what —

[Students speak over one another]

Professor Michael McBride: They all have to do with navigation, with making England strong at sea. Now back here is another science, Chemistry. That doesn't seem to have anything to do with navigation. Why would Chemistry be important to Charles?

Student: War.

Professor Michael McBride: Look at it.

Student: War.

Professor Michael McBride: To make gun powder. There was a chapter about gun powder in The History of the Royal Society. Okay, and up here at the top is the motto, which is Nullius in Verba, which comes from this quote from Horace, and what it says is, "Lest you ask who leads me, in what household I lodge" (that is, what philosophy I advocate) "there is no master in whose words I am bound to take an oath. Wherever the storm forces me, there I put in as a guest." So it's the experiment, not the philosopher, that leads you to the conclusion. So Nullius in Verba is 'in the words of none.' And, in fact, the original name of The Royal Society was The Royal Society for the Improving of Natural Knowledge by Experiments.

Okay, so we're going to see, as the course goes along, important experiments that really decided questions, and in fact Bacon's most important kind of experiment was one that "finally decides between two rival hypotheses, proving the one and disproving the other." So you can do all sorts of experiments and just be collecting butterflies — no, I don't mean to insult people who collect butterflies, it's a fine thing to do. But there's something special about experiments that really are designed to answer a question. Now Bacon devised a name for such experiments, and they're based on this model, that you have a road that diverges and you need to know which way to go between these two hypotheses. What do you need, to know which way to go? You need a sign, or this was a cross that you mounted at a crossroads. So the Latin name for cross is crux. Do you see what they call the experiment? Crucial. That's the origin of the word crucial, right? It's the one that tells you which way to go. Okay, so here is Isaac Newton and he's holding something. Can you see what he's holding in his hand?

Student: A candle.

Professor Michael McBride: I'll give you a hint. It's a prism. Why is he holding a prism? Because that was his crucial experiment; and here's his diagram in that experiment with a prism in it. He called it the Experimentum Crucis, taking the word from Bacon. Okay, so light came in through a hole in the window, through a lens, and then got bent and dispersed into the different colors. So you get a spectrum here on this thing, the different colors. Now there's the question, how does the prism make color? Hooke and Descartes thought that light was a train of pulses and as it goes through something like a prism, or as it reflects from a thin layer of oil on water or something like that, that it changes the timing of the pulses and therefore changes the color. But Newton thought that the colors were pre-existing, and the prism just separates them. And this was his crucial experiment to decide between those two theories. You see what he did? He drilled a hole through the board and let through only the red light, and put a second prism there. And he wrote here, three times — he wrote it here, and also here, and also here — nec variat lux fracta colorem; which means "the broken light does not change its color." So this proved to Newton, at least at that time, that light is a substance, not a train of pulses. What do you think of that proof now? You think light is a substance or a train of pulses?

Students: Both.

Student: Neither.

Professor Michael McBride: But at least you can see that in terms then, that was a crucial experiment, a really important experiment, and that's the kind of experiments we'll try to talk about in the course. Experiments are indispensable in Organic Chemistry. It's an empirical science based on observation, and that's why you have to take the lab. But so is logic — that was number three and number four of the ways of knowing — logic is important too. So believe what I tell you here only when it makes sense to you. Don't just cram it in, make sure it makes sense. But what if it doesn't?

Chapter 4. How to Succeed in Chem 125: Following Samuel Pepys [00:30:15]

Now here's how to succeed in Chem. 125, and we'll take as our model science student Samuel Pepys. How many people have heard of Samuel Pepys? Have you heard of him as a scientist?

Student: I don't remember.

Professor Michael McBride: What did you hear of him as? What do you associate with Samuel Pepys?

Student: Newton-Pepys Problems.

Professor Michael McBride: Right in this period, in the heart of the science growth. But what you know him for was his diary, which tells all about life, everyday life in Restoration London. He was actually, as a sixteen-year-old, present when Charles I was beheaded in 1649. Now what's the connection? Do you know where this is? Anybody been there? Dixwell, Goffe and Whalley Avenues, those are named for three of the 50 judges that condemned Charles I to be beheaded, and they were the only ones that lasted very long, after the Restoration, and they lasted because they fled to New England and were hidden on West Rock. All these roads are heading west toward West Rock. Okay, so that's a tie-in to the same period. But anyway, he got his B.A. in Cambridge in 1654 and a Master's in 1656. And he got a good job, he became Clerk of the Acts for the Navy Board, which meant he was the guy that purchased everything for the Royal Navy, all the rope, all the tar, all the lumber and so on. And on July Fourth, 1662 — it's the fourth of July but it's more than 100 years before that became relevant — he writes in his diary, "By and by comes Mr. Cooper, mate of the Royall Charles, of whom I intend to learn mathematiques, and do begin with him to-day, he being a very able man… After an hour's being with him at arithmetique (my first attempt being to learn the multiplication-table); we then parted till tomorrow."

So here was the guy doing all the purchasing for the Royal Navy and he didn't know multiplication, let alone division. But he worked hard at it. July ninth, five days later: He's "Up by four o'clock, and at my multiplicacion-table hard, which is all the trouble I meet withal in arithmetique." He can do the other things pretty well. July eleven: "Up by four o'clock and hard at my multiplicacion-table, which I am now almost master of." Christmas — so six months later: "…so to my office, practicing arithmetique alone and making an end of last night's book with great content till eleven at night and so home to supper and to bed." Or a year later — so he was motivated and he was diligent; that's good. A year later, on a Sunday: "…I below by myself looking over my arithmetique books and timber rule. So my wife arose anon and she and I all the afternoon at arithmetique," [laughter] "and she has come to do Addition, Subtraction and Multiplicacion very well, and so I purpose not to trouble her yet with Division…" Right? [Laughter] So he worked with a study partner, and that's crucial. And Isaac Newton — does anybody recognize this book?

Student: Yes, sure.

Professor Michael McBride: Right? The Mathematical Principles of Science, of Natural Philosophy. But there's an interesting thing on the title page. Samuel Pepys is the one who gave permission to publish that book, because he was the president of The Royal Society. Now six years later Pepys encountered a problem with dice. The reason was he went to coffee shops every night for dinner and they'd gamble, and people proposed various kinds of bets, and he couldn't figure out this one, so he wrote Newton for help. So this was the problem that he wrote to Newton, twenty-second of November. So A has six dice in a box, and he has to throw a Six by throwing it; B has 12 dice and he has to fling two Sixes; and C has 18 Dice but he has to get 3 Sixes to win. The question, "Whether B and C have not as easy a Taske at A, at even luck?" That is, if the dice aren't loaded or anything, who has the better bet? [Laughter]

How many people think that it's the same? Don't be shy. How many think it's A? How many think B? How many think C? How many don't really have any opinion at all? Good, that wins. Okay, so he wrote this letter to try to get help on his bets from Newton, and Newton replied, four days later, "What is the expectation or hope of A to throw every time one six, at least, with six dyes?" So you get two sixes you still win; that wasn't clear in the original statement. So he says, "If we formulate the question that way, it appears by an easy computation that the expectation of A is greater than B or C; that is, the task of A is the easiest." There's the answer. So Pepys replied on the sixth of December: "You give it in favour of the Expectations of A, & this (as you say) by an easy Computation. But yet I must not pretend to soe much Conversation with Numbers, as presently to comprehend as I ought to doe, all the force of that wch you are pleas'd to assigne for the Reason of it, relating to their having or not having the Benefit of all their Chances." So he wasn't ashamed to admit that he didn't really understand — that's crucial. "And therefore, were it not for the trouble it must have cost you, I could have wished for a sight of the very Computation. "

Can you show me how to figure it out? And he wanted that because somebody might change the terms of the bet and then he wouldn't know. He wanted really to understand. He insisted on proof. So this is two of the pages from Newton's correspondence of the letter that he wrote in response, and you can see that Pepys certainly got more than he had bargained for. "So to compute this I set down the following progressions of numbers." So you can go through all this and you get complicated quotients here, and it turns out that A has 31,031 chances out of 46,656, or 0.6651 chance of winning, and B has this, which is 0.6187; A wins. So is Pepys satisfied with this? Pepys writes back and he says, "Why?" Right? "I cannot bear the Thought of being made Master of a Jewell I know not how to wear." So he's willing to swallow his pride to search for really solid understanding. Now compare this with a comment we got at an end-of-semester evaluation in January a year ago. "I never went to his office hours for help because I felt like he would make me feel stupid, because he's superior to me in chemistry." I hope I'm superior to you in chemistry. [Laughter] I'm not superior as a person, but I hope I'm superior in chemistry. You're paying me the big bucks because of that. So swallow your pride and ask someone for help. Follow Pepys.

So read "Pepys and Newton" and get together to do problems for Monday, and contribute to the Wiki when you're asked to do so. So here are problems. For Friday the problems are optional but very helpful. One is find out which two class members have the rooms nearest you so that you can maybe use them as study partners. You don't have to use them, use anybody, but use someone, don't try to go it alone. Two. What are the three most common items of advice from course veterans? So if you click there, or go to the webpage, you can get anonymous advice; I was careful to make sure it's anonymous. So you can get all — much of it is contradictory, so your job is to look through it and try to get some idea of what they're telling you that's worth knowing. For Monday there are problems from that webpage, "Pepys & Newton." And let me tell you that you better get together with other people to do it, because there's a lot of stuff there. So get together in a group, parcel out who works on what, discuss what went on and so on. And then for a week from Friday there's stuff about drawing Lewis Structures, from another webpage about functional groups. So we'll get to that later, I just wanted you to know what's coming up. Incidentally, this thing about the problems set that has to do with the mathematics that Newton and Pepys were working on there, has to do with isotope ratios. You know, chlorine has a funny atomic weight. Why? What is the atomic weight, does anybody know?

Student: 35.5.

Professor Michael McBride: Thirty-five and a half. Why a half? Most of the elements are pretty near integers. It's because it's a mixture of isotopes. It's a quarter of one isotope and three-quarters of the other, and the average is thirty-five and a half; thirty-five and thirty-seven. But in fact it depends on where you get chlorine from, what the ratio is. There's thirty-five and a half for a standard atomic weight, but it ranges quite a bit, depending on where you get it. So by measuring these ratios, which is a lot like these odds in the betting, you can tell where things came from. You can tell where hydrocarbons came from sometimes that way. And those are the problems that you have to deal with. So it's not really very, very relevant to the course as a whole, but it's relevant to the Pepys and Newton thing and it's a fun problem. So that's what you've got to do for Monday.

Okay, and here are the assignments. I emailed all these people. I hope you're here, and that you picked up on what we talked about today so that you can improve the Wikis from last year. Last year people developed their Wikis from scratch. This time — which is a very valuable thing to do. So I was torn this year as to whether to have you do them from scratch or whether to modify last year. I figured modifying last year is better because then you have something to read earlier on, for those who are not working on developing it. So anyhow, but the hope is — so if you modify it — it has to be something significant, not put a comma in or something like that, but add something useful to understanding. If you do it within thirty-six hours, you get two points, and if what you do is really good, you get three points. So you go to that page and you click on those things and then you can read what — or you can either modify them or read it; it's a Wiki.

Chapter 5. Atoms, Molecules, and Hooke's Law [00:41:56]

Now, we come to the question that we'll address more. We have another five minutes here. The question we're really dealing with now, having seen how to work in Chem. 125, is are there atoms and molecules; how do you know? And what force holds them together? Because if we knew that they're real, and we knew what force held them together, then in principle we might be able to calculate everything. So it would all be theory. So is it springs that hold atoms together? So Robert Boyle — notice he's right at that time, 1627 to 1691, and he's the oldest person that's on the Honor Roll outside the building here, he's over that way — so Robert Boyle wrote this first important book in chemistry, New Experiments Physico-Mechanical: Touching the Spring of Air. So you know Boyle's Law, how pressure and volume change, that air in a piston acts like a spring. So PV is a constant; that's Boyle's Law. So he developed this science on the basis of a new instrument, the pneumatical engine, which was built by Robert Hooke, the guy we quoted. And there's a picture of the air pump here with that crank on it, and so on to pump things in or out of that bulb. Now a couple of years later Hooke wrote this book, Lectures, De Potentia Restitutiva, or of Spring, explaining the power of springing bodies. And this is the beginning of that book. "The Theory of Springs, though attempted by divers eminent Mathematicians of this Age has hitherto not been Published by any. It is now about eighteen years since I first found it out, but designing to apply it to some particular use, I omitted the publishing thereof." So he kept it secret so no one would steal the idea. What did he hope to do with a spring, a really important technology that he could do with a spring? There was a coil in the spring that he depended on.

Student: Flying.

Student: Pendulum clock.

Professor Michael McBride: A new kind of clock, one that could work better for navigation. It was his spring that actually allowed Harrison, 100 years later, to win the contest about making an accurate clock; some of you must know that story. So anyhow he had been hiding this so it wouldn't be stolen. In fact, it was stolen by Huygens. So "about three years since His Majesty was pleased to see the experiment that made out this theory, tried at White Hall, and also my spring watch. About two years since I printed the theory in an anagram at the end of my book on the description of helioscopes, viz." this. So this is what he published at the end of this book on helioscopes, and that is an anagram of how springs work, so that later he could prove that he knew it, if needs be, but no one could steal it in the meantime. And if you unscramble it, it's "Ut tensio sic vis; that is, the power of any spring is in the same proportion with the tension thereof. That is, if one power stretch or bend at one space, two will stress at two, three will bend at three, and so forward." So here's his figure that shows that. That's Hooke's Law, the force law. The force is proportional to the distortion. So here's his figure, and he's got plots of it here. Ut tensio (as the extension) sic vis (so the force). So it's linear, the force is how much you stretch it. And he has lots of different kinds of springs that do that. Here's this clock kind of spring, a coil spring, just stretching a wire. So the force is proportional to the extension. Or another way of saying it is, "The potential energy is proportional to the square of the extension." So it's a parabola. So that's Hooke's Law, and that's where we'll take up next time.

[end of transcript]

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CHEM 125a: Freshman Organic Chemistry I