By Douglas J. Shaw, Ph.D.
Introduction The following are notes on a talk I gave August 7, 1995 at the Geometry Center, to some young summer institute participants preparing to make their final project presentations. I've rewritten these notes to make them coherent to all of those people fortunate enough not to be me. Be warned, if I had to decide between putting down what I actually said, or what I shouldda said, I often choose to do what most UN translators do. I also restored a few sentences which I had cut for time reasons. If you wanted to know what was said verbatim, you should have come to the talk. Any questions, comments, feedback, or monetary contributions should be sent to Doug Shaw c/o the Geometry Center. The talk began with Tony Phillips: "Doug comes to us from the University of Michigan, where he just received a Ph.D. in combinatorics. He is also a successful veteran of many public speaking contests, and has emceed the annual Ann Arbor Monsters of A Cappella concert. Here's Doug..." The relevance of this will be explained later.
Raise your hand if you've been to a bad talk. [Most raise their hands] Before I begin I'd like to say that the talks I've been to here have been consistently good. But don't get spoiled. As the people who raised their hands can attest, outside of this wacky wonderful gestalt we lovingly call the Geometry Center, the quality of talks varies greatly. This gives you an opportunity. If you can give great talks, then you will always be in demand, regardless of your subject matter. What I would like to do is help you to make your good talks into great ones. [Hand out blank outline]
A) The first question
Before you even begin writing your talk, there is one question which you should ask yourself. Answering it carefully will make the rest of your preparation go a lot easier. Anybody know? Tamara [Munzner] said it on Friday... [Audience participation. Pay $1.00 to first participator, and comment on how the first person to speak does you a great service] The question: "What am I trying to accomplish?" Is it to entertain? Get people up to speed so they can do research? A sentence like "Tell people about measure theory" is not the "point" of a presentation; it is the topic. You need to figure out what you want to accomplish by telling people about measure theory. (Obviously "entertainment" will NOT apply here.)
The goal of most math talks is to advertise a topic; to give people enough of the flavor of what you've been doing so they can decide whether or not they want to read your abstract, read your paper, collaborate with you, or (God forbid) renew your funding. And a talk where you are advertising a topic should be different than a talk where you are preparing students for an exam.
When I asked myself the question for this talk, I came up with, "This talk is to give you some tools to help you give even better talks in the future."
1) Is rehearsal worth the effort?
I would answer this question with a "yes." not only for the practical reasons, but for a philosophical one. It's a respect issue. If I give a talk to you, and I didn't take enough time to prepare it, what I'm really saying is that my time is more valuable than all of yours combined. Paul Erdos could probably make that statement, but I don't think any of us has that right.
By running through the thing at LEAST twice you will get the kinks out, and see how the time issue is going to resolve. For example, can anybody guess how long the first edition of this talk timed out? [Ask for guesses] It took an hour and a half. So I had to cut a lot out, because I wanted this talk to last for thirty minutes, to leave time for the more experienced people to add their comments and for us to have a discussion.
Note that your talk will go slower the larger the crowd. It takes them longer to react to what you say. If you make a joke, the laughter (or angry silence) will travel over the crowd like a wave, as the people who didn't get it start to laugh after their neighbors do. If you are miked, then the echo effect will also force you to speak slower. This talk took about twenty to twenty-five minutes in rehearsal, so I am estimating thirty to thirty-five minutes in practice.
2) Who are these people?
You absolutely gotta take the crowd into account. If you want to freak yourself out sometime, ask an audience what they think of your speaking rate. If you're on the East Coast they'll say you talk too slow. If you're in Urbana, Illinois they'll say you talk too fast.
What kind of audience do you get at most math talks? Usually they are smart people. Their mood will range from mildly supportive to mildly indifferent. At a Calculus reform talk, you will have the zealots sitting here, and the openly hostile sitting here, which necessitates a very different style. At the Geometry Center, the audiences seem to be very curious and wired.
I had to change this presentation over the weekend because this audience changed. Most of you saw Tamara's talk last Friday. I was going to give a description of what a good, polished talk looked like, but since you've just seen one here, it would be redundant. Furthermore, a lot of what she discussed overlapped what I was going to say, so I excised that material outright.
3) What should I include?
The first question should be your guide. If you know what your goal is, then take out anything not directly related to that goal. There is a fundamental paradox that is very important. [Raise screen. The following is written large on the white-board: "The fundamental paradox: The coolest stuff happens only after a lot of background, but if you rush through the background, they won't understand the coolest stuff."] How do you get around the paradox? I don't know. It's subject specific. But you must address this issue, and not ignore it. Otherwise, you fall into the trap of having the last five minutes of your presentation consist of your audience ooohing and ahing over some beautiful graphics you show them, without getting anything real out of it. (Note: If the purpose of your talk is merely to get them ooohing and ahing, of course, this may not be a problem. It all depends upon what you want to achieve.) If you take nothing else away from this talk, this is what I want you to remember. That's why I've written it big like this; it is important.
1) Get someone to introduce you if you can
Before you say your first words, you want to establish your credibility as a speaker. The introduction that Tony gave me was ideal for this talk. He told you I had a Ph.D. from Michigan, so you (hopefully) believe I am qualified to talk about mathematics, and he told you about the speech contests, so you know I am qualified to talk about speaking. I knew he would give me a good introduction, because I wrote it myself. Be aggressive with your introducer. Before you talk, take him or her aside and say, "When you introduce me, please include this, and this, and please don't include THAT."
The only thing to be careful of is if the person who is introducing you is inexperienced. One of the most embarrassing things that ever happened to me occurred several months ago, in Ann Arbor. Due to an odd chain of events, I was scheduled to appear on a live television show with a Swami. I did a little research and found out that he was fronting for [a cult leader] in India. Whenever he spoke, he used his Michigan Ph.D. for credibility. I thought I might wind up confronting him so I asked the host, Mike B., to mention the fact that I just got a Ph.D. when he introduced me. (I wanted the Swami V. and I to be on equal footing.) I didn't take Mike's inexperience into account, thought. He introduced me this way, "My next guest is Doug Shaw, who asked me to make sure I told you that he just got is Ph.D." [Hopefully laughter will ensue. Pause while it dies down. If it doesn't ensue, act as if it wasn't expected and hope no one catches on] I was mortified. But in retrospect, I didn't handle it right. What I should have done was, in conversation with Mike, mentioned my Ph.D. and then hoped he'd mention it. Inexperienced emcees tend to grope for things to say, so if you can get the information you want announced to be fresh in their mind, there is a good chance it will come out.
2) Get some attention
I would like you to compare the following first lines of a talk: "I'm going to say some kinda basic things about projective geometry, so let P be a plane..." versus [Adopt over the top posture] "Hello. I'm Matt and it is my mission to sell projective geometry to the world! Projective Geometry is important because..." [If audience seems into it, get a bit of discussion going here]
When Matt gave that talk recently, I had not been really excited about projective geometry. But after that sentence, I, and I suspect most of you, were primed and ready to hear what he was going to say next.
You want your first line to really grab your audience. Don't start with an apology. "Hello. I'd like to start by saying that I didn't really have time to rehearse this like I should have, and I'm sorry the drawing are so bad, and that most of this is 10 years out of date. Now let P be a plane..." Oh, man. Don't apologize. If the talk is going to be bad, you don't have to tell us. Trust me, we'll figure it out.
A young poet ran into Oscar Wilde at a party. Oscar complimented him on one of his poems. The poet said something like, "oh, well, it didn't really achieve what I wanted, but the meter was fair..." Oscar interrupted him angrily, "Oh, don't act humble; you're not THAT great!" Good advice for us, too. Be bold! That way, if you fail, you will at least fail spectacularly.
I started this talk by getting people to raise their hands and talking about bad talks and market demands. I was hoping to grab your attention by making you move physically, and by talking about future careers. Whether it worked or not, you will have to tell me, but that was my goal in opening this talk the way I did
3) Give them a road map
Before word one is uttered, you audience has three questions. Who are you? What are you going to be talking about? Why should I care? Hopefully, you will have gotten someone to introduce you and answer the first question. Otherwise you may have to sneak a word in subtly. But in any case, if you take a full five minutes of time to make sure the audience knows exactly what you are going to be doing, and why it is important, you'll find that it is easier to keep them with you as you go.
Proving a theorem is different than relating a story, or telling a joke. It sometimes works better if you give away the ending beforehand. (Having said that, I do confess that if the end result is really counter-intuitive, and I'm feeling self-indulgent I might end my introduction with "...which will lead us to a very surprising result." If you do that, make sure you are confident that they will agree - you are putting yourself on the line.)
1) The Nerves
I have a quick question for all you psychics in the audience. How am I feeling... right now? [Do the classic newage "sending" posture. Wait until someone guesses. If they are right, wrong or close, tell 'em so] Nervous is close. Terrified is better. This is my first talk in front of my colleagues. If I screw up now, I'm still going to have to work with you for the next two years. Furthermore, my boss [Point at HK. If he isn't there, point at Tony] is right there. In a few days, I am going to be working with some of you on improving your presentations, and if you see me blow it now, my credibility is shot. [Improvise here. There are lots of perfectly good reasons to panic.]
It's important that you believe me here, so I am going to demonstrate. [Take meter stick. Hold it out as steady as possible. Let audience laugh at how it shakes.] What is happening in my body right now? Adrenaline is pumping throughout to give me the energy to either slay you all, or escape. Let's see. The first... [Look at audience considering it] I could probably take you on, if it weren't for this guy/gal. [Point at toughest looking man/woman] As far as the second... there's no way I could make it to the door in time. So I have all this energy coursing through me. Now my society has taught me to turn it inward. So what can I do? [Demonstrate the ol' fidgeting, tugging at clothes, hair, etc. If they laugh, milk it a bit]
What I want you to do is to learn to take that energy and push it outward. If you were going to make a gesture like this, instead make it like this. If you were going to point this way, instead point this way. If you were going to speak at this volume, instead speak at this volume. The audience will think you are confident, instead of terrified. When I did the speech contests, I was told I improved at every level. The reason was because the larger the audience, the more terrified I became, and people mistook my terror for confidence and strength. Trust me, it works. This [Point at fundamental paradox] is the most important thing I'm going to tell you today. Channeling your nervous energy is a close second.
2) Pause, damn you! Pause!
After showing a fifth level Basango surface STOP! Stand up. Point out stuff with the pointer. I KNOW you want to show them all the cool pictures, but they're only going to remember a few anyway, so pick and choose. You've been beating your head against this picture for months. They've never seen it before, and may even need your guidance to see what about it is unusual or interesting.
When you say a Basango surface is the result of sewing a cartioid to a centipede, everyone listening is now mentally trying to do it. And I, for one, am not going to give you my full attention until leg #100 of that centipede is on that cartioid.
Pause after EVERY definition, and after EVERY claim.
A rule of thumb for how long to pause is this: Pause as long as you comfortably can, and then count three more "beats."
3) Extra things to put on handouts
I don't think an overhead display can hold a candle to a good handout. People can write on their handouts, and refer to them. Be careful about putting too much in them, because you don't want them to be a distraction. You may want to include definitions and a basic example or two that you want them to be able to refer to. When I give talks about my research, for example, I start by defining difference sets. If you forget that definition, then the rest of the talk becomes meaningless. So I always have that definition nice and big on a handout, along with an example of a difference set. So if anyone gets the question, "Damn, what was a difference set again?" they can look down and go, "Oh yeah, right, I see." And, if I make any statements about difference sets they disbelieve, they can look at the example and check it for themselves.
4) Kill those qualifiers!
I know that as mathematicians we like to be precise, as do chemists, engineers, and physicists. Well, maybe not physicists. But still, I would like to show you a sentence that I've heard three different people use in talks practically word for word. [Say and write on board] "I have tried very roughly to draw what it would look like to a flatlander." Let's count the qualifiers here. "I have tried", "roughly, "very roughly". Let me tell you a secret. [Check door to make sure Dick and Arnie aren't listening. Whisper loudly:] Flatlanders don't really exist. No flatlander is going to appear and say, "That isn't what it looks like to me at all!" [Cross out qualifiers, to make it read "This is what it would look like to a flatlander."] There. This means exactly the same thing as the first. If the picture is rough... trust us, we'll know. If we don't, then you've gotten away with it, be happy. Make your assertions carefully, sure, but also make them boldly.
Remember the first question. Unless the purpose of the talk is to give an exact, precise, understanding of a concept to the smallest detail, you don't need all of those distancing, butt-covering words. And if you really want to convey knowledge that precise and detailed, I would put it to you that an oral presentation may not be the best way to achieve that goal.
5) The evils of technology
There is an interesting option at the Geometry Center that many people take advantage of: using the computer while having the CRT projected on the movie screen. There is a problem with this however. Let's look at it from the audience's point of view. I claim that giving a talk while sitting at the terminal and using the projector is isomorphic to showing them a video with a voice over. Worse, since you are doing it in one take and rendering images on the fly, it is a bad video with voice over. I'm not saying not to use this tool, indeed it is essential for most talks here. But we have to think of ways to get around the inherent problems with presenting in this way.
When I gave a talk to the Early Alert kids, this is what I tried: I did something at the terminal, then ran over to the screen to point things out, then sat down and did more, and got up again. [Demonstrate as this is said] The problem was that the running back and forth was tiring to me and distracting to my audience. "Look at the funny hyper man talking to us!" [Take out pointer] One of these helps a bit, halving your distance. And the Geometry Center has a box of them in the supply cabinet.
Another method is to carefully structure your talk so you can be up front for a bit, do a chunk on the computer, stand up for a bit, etc. Breaking it up without having to run back and forth rapidly.
I think the best thing to do is get a partner, and rehearse it a few times. A great example of that was Thomas and David's talk. Thomas stood and spoke to us, while David manipulated the images. Anyone else see that? [Wait for response] They had it down to a point that was scary, like Thomas was activating a touch screen.
One method I really like is trying to use low-tech demonstrations. Remember when Matt used this lamp to demonstrate the deformation of the ellipse to a parabola? Of all the talks I heard that day, that is what I remember the most, and I suspect that is true for you too. When you demonstrate with ordinary objects, it is easier to remember, and you can go home and repeat the demonstration for yourself. Matt could have whipped up a quick computer demo for that concept, but I don't think it would have been as effective for me.
6) Using notes
To use notes, or not to use notes? The answer is clearly that you should ideally memorize everything, and not need notes. In practice, however, especially in a technical talk, you will probably wind up needing them. But there are effective and ineffective ways of using notes. You want to avoid this: [Bend over and squint at notes] You want to make them big. Here is a page of my notes for this talk. [Hold'em up. Ask person in middle of room if s/he can read them]
Seeing them should not even be an issue. Print on one side, not two, so you can turn the pages this way, not this way.
7) Any questions?
What is the mathematical synonym for "Class Dismissed?" [Hopefully they will all shout out "Any questions?" If not, tell 'em] Regarding questions, I'm going to ask one main thing of you. you have to learn to love them. I love it when someone asks me questions. If I know the answer, it gives me a chance to show off. In fact, I'll sometimes even pause dramatically, look up a bit, [Overact a bit] and then shoot off this impressive answer. Even if you don't know the answer, the fact that someone asked a question means that in some way your talk aroused curiosity and you should be flattered. Also, the old saw is true: If one person asks for clarification, probably 5 more are also confused.
One of the best ways to foster questions is to leave time for them. If someone asks for questions 57 minutes into a "50 minute talk", nobody is going to want to ask any.
There is one phrase which most people in our field really hate to say. It is something we all should say, at least once, so on three I'd like you all to say, "I don't know." One, two, three... [If less than 100% do it, make 'em do it over] I once suffered through fifteen minutes of somebody working at the board, desperately trying to answer a question. It was painful for everyone involved, and no one cared about the answer any more. He should have just said, "I don't know, I'll get back to you," and worked it out later, under less pressure.
The only time where "I don't know" may not be appropriate is your Oral Exams, but even then, the guideline at Michigan was, "You can say, 'I don't know,' but you can't say it too often."
Occasionally you will have to deal with antagonistic questions. I'm going to give you three techniques to help you, two of which I think are ethical. The main idea is that if someone asks an antagonistic question they expect to be listened to, and if you just brush it off, you will look bad and the question might be pursued.
The first thing to do is politely defer the question. This is a very sincere technique. Point out that you heard the question, but it's outside the scope of your talk, or that you don't have the time to give the question the attention it deserves, but you would love to buy the questioner a beer and talk about it some time. The alcohol bribe works better than you'd think. This works best if the question is antagonistic, but the questioner is fundamentally friendly.
I learned the next one in debate class. I call it verbal Judo. the principle is that the main thing a smartass wants to do is... well... look smart. So what you want to do is put him in a situation where the ONLY way he can look smart is by being on your side. The best way to do this is by example. Who here is really arrogant? [Pick someone, hand him a piece of paper that says, "This is all well and good, but how could you prove this in a rigorous way?"] Okay, now in your most arrogant voice, ask the question. [Asks questions] Hmmm. What would you suggest? [Said in a sincere voice]
Now think about *'s position! He could say he doesn't know, but then he would look bad. Or, he could give you some good advice. Either way, the question is not his problem anymore.
There is another technique that works for confrontational people, as opposed to arrogant people. I learned from a negotiation skills workshop. I didn't believe it would work, but then I tried it and it did, but now I've stopped using it because it's a little unethical and scary. Like black magic. The idea is that when someone confronts you, the word they want to hear more than anything else in the world is "Yes." That's it. So you give it to them. They you follow it with "and." You can't say "but" because the phrase "Yes, but" means "no." So you say, "Yes and," and follow it with whatever you want to say. The confronter will just hear the "Yes and," and the audience will just hear the bit afterwards. Let's demonstrate. [Give paper to person] Okay, we are going to pretend that I just demonstrated a brilliant technique that solves the three body problem. When I finish * is going to read the question in a really confrontational way.
...and that is my technique for solving the three body problem. Any questions? [* reads, "Surely this "technique" of yours would be worthless if you tried to extend it to more than three bodies?"]
Yes, and in the three body case my technique completely predicts the behavior of each body, with a minimum of computer time, and an almost complete amount of generality with regards to initial conditions and...
Your antagonist will be happy after the "Yes" and not listen to the rest. The audience will not even remember the question. I can tell you don't believe me. Tell you what, next time you are arguing with somebody, try this method and tell me if it works for you. You will find that it does word, but in a weird mind-controlly sort of way.
"This car is ugly."
"Yes, and it has great mileage and a good warranty."
[Like a hypnotized person] "I agree. Let us buy it."
I have used this method in heated discussions and it has worked. Don't tell anyone. [Good thing this talk will never go on the Web!]
E) Closing it up
You've just given an excellent talk, there is a roomful of people who want to write papers with you, and a talent scout for the NSF wants to give you a large check. All that's left is wrapping it up...
1) Bad phrases
A couple of things you want to avoid in your conclusion. Never end with an apology. Remember what Oscar Wilde said. Don't go, "So that's my talk. I'm sorry it was so bad. Any questions?"
If you say, "One last thing." That's IT. No More! You've started the clock. I try never to use the phrase at all, because sometimes I think of something right at the end. But if I do slip and use it, I know that I had better choose that last thing with care.
2) Good things to include
As we've said before, make sure to leave time for questions. References are a good thing to include. There is always a chance that people are going to want to learn more about the subject, especially if arousing that interest was one of your goals. So you are doing them a service by pointing them in the right direction.
Another thing that people like is for you to fit your work into a larger context. How does this theorem affect your specialty? How does it affect mathematics? How does it affect the world? I have to admit that this is where I'm weak, in that I usually don't care enough what my interests can be applied to. In fact, when people ask me, "What can this be used for?" no matter what I am talking about I usually say, "Quantum Groups." Most people don't know anything about Quantum Groups, and like to pretend they do, so they nod and go, "yes, I can see that. Quantum Groups." This bluff does NOT work if the person works with Quantum Groups. For those people I say, "Communications Networks." No human being understands both of these subjects. I'm not advocating you bluff like this, of course, but be prepared to be asked to fit your work into the scheme of things if you don't put it into your conclusion.
Another good thing to mention is your plans for future development. This accomplishes two purposes. First of all, it is of kind of "marking" your territory, if you want to view it that way. More importantly, it may encourage future collaboration. Someone may very well be working in the area you are moving towards, enabling you to meet in the middle.
Try asking for "Questions or suggestions" instead of questions. This tends to get a good discussion going, and questions will be asked as a result.
Tamara ended her talk with an amazing phrase which worked very well. I can't advocate it yet, because I haven't tried it for myself, but I will the next time I give a math talk. If you want to try it, please let my know how it goes. She asked for "Questions or feedback," and what followed was really stimulating.
In my opinion, both of these phrases work because rather than putting you up on a higher level, which subtly intimidates or annoys people, they let you acknowledge that you respect your colleagues, which makes them more likely to want to interact at the end.
At this point I would normally ask for questions, suggestions, or feedback, but first I would like to introduce Tony Phillips. [Read introduction] [At this point, Tony gives any additional comments or feedback, and then we throw it open to a discussion. Ideally, when the smoke clears, everyone will have learned and had a good time, and nobody will have gotten hurt.]
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