Women of MIT: Celebrating Science and Engineering Breakthroughs (Session III)

CHISOLM: I'm Penny Chisholm. I'm chairing this next session, and I would like to add my voice to the chorus of thanks, to Ed for organizing this, and also to Nancy for everything she's done for women faculty at MIT over the years. She's really absolutely changed our life. I referred to the initial group in this study as the uprising when I talk about it with my colleagues around the country, and they've all watched the progress here, and it's largely due to Nancy's leadership and the fantastic administration that joined us in that activity.

So now we have three exciting talks that cover the cosmos, tiny swimmers, and patterns in language. And that's just so MIT when I think about it. So our first talk is by Regina Barzilay, who's an associate professor of electrical engineering and computer science, has degrees from Ben Gurion University and a Ph.D. In computer science from Columbia. A number of awards-- National Science Foundation, a career award, the Microsoft Research Faculty Fellowship, and also she received the MIT Technology Review Young Innovators Award for young innovators under 35. She's going to be talking today about teaching machines to behave using natural language.

[APPLAUSE]

BARZILAY: Thank you for the introduction. So my field, my general field of study is statistical natural language processing, and I'm sure many of you are familiar with this field, primarily from the Hollywood perspective. We have a very long time from '30s, we had machines which can understand us and speak to us in natural language. And for quite a long time, we've seen natural language technology only in the movies.

Luckily for us, in the last decade, the situation changed, and now we've seen some really interesting technologies that are used by millions of people. So one example would be Google Translator. Maybe a month ago, you've seen the question answering system from IBM, Watson, which won Jeopardy game against human champions. Many times you are using natural language technology even without realizing that you're using it. So one of the examples is SAT scoring, which from 2003 is done using statistical natural language processing techniques.

So one question you can ask yourself-- what exactly happened here that this technology was nowhere in real life and all of a sudden, it moved towards real applications? It's actually very interesting when you look at the change in technology within the field. So when artificial intelligence was very young, people had this naive idea that you can take the computer and feed it with all the human knowledge, and if you put enough knowledge into the computer, you would be able to make a computer which can understand language. So people feed grammar, people feed dictionaries, and each word for very, very small domains. And the hope was, OK, let's just add a bit more and a bit more, and then the computer will start understanding language.

So guess what. For 20, 30 years, they tried, and it never was able to really understand language or to scale up. So it was sort of a spectacular failure in the wrong scientific methodology. And when I took the first time natural language processing class, the professor couldn't show me even one system that was working. And then a great thing happened. In the mid-'90s, the field underwent statistical revolution when technology completely changed.

Rather than trying to feed the machine with the knowledge, the idea was that we can give the machine a lot of data, and machine would be able to infer the right knowledge from this data. So this is called machine learning. And let me be more concrete here. Let's say you want to design a program, which given a review predict whether it is a positive review or a negative review. This is a very simple task that machines can do very well.

So here you can see one positive review and one negative review, and you can see that they have different words in them. Correct? So if we don't want machine to fully understand English, but we still want it to solve this task, what you can do, you can say, maybe the machine can just analyze the distribution patterns in both cases, and predict which distributions are more likely to appear with positive reviews. So you can have one example, two examples, three, and four. You would see that there are certain spikes and certain words which are positive and the words which are negative.

So the way to sort of formalize this intuition is to think about every text as one big vector, and for every word in English you can have an entry in this vector, and if the word is present in the text, you would [? pull ?] one. Otherwise, zero. And for each one of these vectors, you can say, does it have positive or negative sentiment? So for those of you from the field of science and engineering, it already reminds you you can think about it as a statistical problem. You can just try to fit statistical model, which given enough of those examples, can make predictions about new unseen text and predict their sentiment.

So what we're doing here, we're taking many parameters of the model and adjusting this parameter so that they can do the right predictions. So these parameters would say that, for instance, the word delicious is not only predictive of the positive sentiment. It would also tell how much we can trust this word in relative to other words. So our statistical model will combine all the evidence and make the inference.

So this is obviously a very simple example, and we can apply the same statistical ideas to much more complex mappings. So for instance, machine translation for Google Translator. Here, you can feed as a training, as a data for the machine, instances of parallel sentences. So here you can see a piece of Dostoyevsky in Russian and English. You can imagine for instance [? Babel ?] or [? Europol ?] proceedings, where you have the same content translated in several languages.

And from these kind of data, the machine can lend the transformation, again, using more complex statistical models. Another example here is semantic interpretation you have a piece of text. You have some lambda calculus expression, which encode the semantics, and you can learn the mapping.

So one thing that may be striking for you is that the machine today can translate without actually ever understanding what the word staircase means. You just have a lot of pairs. You learn statistical model. There is no connection to what is going on in the real world. What is the real semantic of the word staircase? And in many applications, you can do it, and you can do it quite successfully.

However, there are many cases where we actually want to make connection to the real world. And my talk today is actually about grounding the interpretation of the language in the real world. So let me give you very concrete examples here. So this is an example of a task, which some of you are [? commentating ?] their own computers doing on weekly basis is installing new software on your machine.

So here, you have some text, which tells you how to install a driver on your machine. And you as a human need to read it and to do the clicks on your machine. So the question, can we automate it? Can we take this piece of text and automatically map it to the right clicks, to make machine do the right thing? So in this case, machine would be very literally interpreting what should be done.

Another example, which is maybe more complex when I'm talking about behavior, is assuming you want the machine to beat for you in some auction, or you want machine to play a game. And machines can do it, but what they cannot do today is to take a piece of text, which tells you what is the right strategy, or take a general human knowledge-- what is good for you to do-- and translate it into the better choice to create a better behavior. So these are the type of questions that I will be talking about-- how we can take a piece of text, interpret it, and translate it into better behavior in reality.

And the idea behind the approach is actually very, very intuitive. You can say, OK, whenever I'm interpreting text, and they really did it correctly, I would assume I will get a good behavior, assuming I have some measure of goodness. So in this case, let's say if I interpreted the extraction correctly, my Windows would behave the way I expect. If I did it wrongly, I may get a mistake in my operating system.

I may crash my computer. So you can try these things in your operating system, see what happens, get a feedback, and then based on this feedback, you can update your behavior. It's pretty much I'm looking at my four-year [? son ?], so this is the way he updates his behavior based on the feedback.

So here, the question is, can we design algorithms that can change the way that interpret language based on the feedback they observed? And here, for instance, for this [INAUDIBLE], the feedback is very, very clear. It would be some concrete reaction from the operating system. And this is sort of a summary of their approach. I'm not going to be blowing off anybody's head, but the idea behind it is actually shown in this cartoon.

Let me be more concrete here about what do I mean interpreting language and acting in the world. So what computer will see at every point will be the state of its, for instance, operating system environment, which windows are open, closed, what you can and cannot do. It will have a piece of text, an instruction.

So at every point, the computer will take one instruction, do an action in the real world, and then the state of the world will change. For instance, here, we will see that some new windows will be open and closed. And then it will continue doing this execution for some time until it gets a feedback, as it would be a failure, or it can be some positive feedback that it succeeded to do the instructions.

And the question is, so I'm underlying you the general frame of the question is how you can actually do the learning. So to give intuition on how you can do the learning, I will take a very simplified view on the problem, but I think it will give a good understanding of the intuition behind the [? mass ?] here.

So you can say, OK, let's say I start with some guesses of what is the correct mapping between the words in English and clicks that I need to do on my machine. And let's make a very simplifying assumption and say that every word is just translated to some click onto some object. It's like one to one mapping.

So now you start with your hypothesis, and you can take a piece of text and translate it using your current hypothesis. You translate it. You can run it on your machine and see what happens. Let's say in this particular case you fail. And you can try and go. You have a very big set of instructions out there. You can actually try to go one after another. In all the cases you fail but one.

So it succeeded with 20% of accuracy. Not great, but you already have some ideas about the mapping. You can say, maybe the parameters which control the translation of this green document, the document in which we succeeded, in this particular case, they were the right ones. The parameters which control the words which appear in all other bad documents, they were the wrong ones.

And I need to update them how to give more weight to the good ones and to detract the weight from the bad ones. And that's the idea. So we're going to change parameters. Try again. So now we have a new mapping, possible mapping. Now we succeeded in two documents, and we continue this kind of update of the parameters based on the feedback.

And what I presented to you here is actually a very simplified description of the policy gradient algorithm, which is a reinforcement learning algorithm. And it does, more generally, the things that I described. It starts with some set of guesses of parameters. Based on these parameters, it selects what is the best action or what is the likely action to take given these parameter values, tries them, executes them, observes the feedback, and corrects the parameters.

And this particular algorithm has very nice mathematical convergence properties, so you can be sure when you are applying this algorithm, you can actually assess how it will behave. So it has a good theoretical understanding of the algorithm. And even though I showed it how you can apply this kind of technique to map the words, and this makes us a bit uncomfortable, we say in general not to translate.

We need to do many more things. We need, for instance, to chunk the sentences into pieces. We need to reorder the instruction, because sometimes we change the instruction or the way we execute them. This algorithm can actually do all this very complex mapping using the same underlying mathematical technique.

So you can do this very complex mapping from the text to the instruction using this nice mathematical framework, where we can try stuff, observe the feedback, and correct ourselves. So I will just tell you how it actually works. So we apply this method to translate Windows 2000 Help documents, so when you have a problem with your machine, Microsoft has a website where you can go, and it will tell you how to solve your problem.

So before I show you the numbers, I want to ask you a question. If you are a person who does this task, you are given the instruction, and you want to go and implement it, how likely do you think human will succeed in this task? Do you think you can do it 100% correctly? A number? Can somebody volunteer a number?

[INTERPOSING VOICES]

BARZILAY: OK. So I will show you the numbers, which are optimistic numbers. Those are the numbers for students in computer science who are graduate students at MIT who do research in systems. If you need an expert, those are the experts. It's like our upper bound in their performance. So they can do this task with 80% accuracy. So how can MIT professors can do this stuff? I'm not sue, but I'm definitely not there.

So you can see that the machine can do this kind of mappings 53% accuracy. And I don't want to make [? hard ?] claims, but I can think of many people [INAUDIBLE] at MIT and outside, which will be able to do it with 50% accuracy, because some of this instruction is actually quite complex. So we can really see that here, this simple feedback and nice mathematical formulation enables us to do this task in a reasonable fashion.

So the first example that they showed you is actually easy example in a sense that here you had instruction from Microsoft, which were written for lay people, where they tell you exactly what to do. Now in how many situations in life are you given such detailed exact advice? Apparently, in very few. You can see there are plenty of books, which tells you how to do things, but they don't tell you every single step that you need to take.

So maybe a more interesting question to ask is, can we take general advice and make machine understand these very general advice? Which is north point to point? Can we get an understanding of this general knowledge? And I will talk about this task in the context of Civilization game. How many of you have ever played Civilization? We see some. We see very few players. It's interesting. Oh, oh, oh. OK. The next speaker plays Civilization. So like if I ask this question to a computer science audience, almost every single person raises his hand.

But the reason that I selected Civilization is because it's a very complex game. It's [INAUDIBLE] a test, because you need to build this whole civilization to grow crops, to fight other nations. You can play it for days and days. And more interestingly, the branching factor, which means what action you can take at each point, the space is huge. It's 10 in the 20s and millions of billions of possibilities. It's almost like you have plenty of choices, and if you want to win, you obviously need to make the right ones. It's a very hard computer game for the machine to play.

So what we want to do is to say, now if I give to machine some knowledge, what are the good moves to take? So for instance, this is a manual, which tells you that if you want to build a city, you need to make sure that there is water nearby, because otherwise, you cannot grow your crops, and your population will starve. The question is, can a machine take advantage of this knowledge?

And before I'm going to go and tell you how we are solving this problem, the answer is we can. Otherwise, I would not have brought it here. But I will tell you how machines [INAUDIBLE] computers can play games. You know that there was like 10 years ago, 15 years ago there was this breakthrough with chess, so computers could play a lot of games quite successfully.

And the way computer plays the games is that they represent the world as a state, so the state is just what do you have in your universe? How many cities? How many people? All the relevant information. And at every point, you can take an action. It's like a play. You can decide, do you want to invade, or do you want to irrigate, or whatever you want to do.

So you start by being in some particular state of the world, and now you need to select an action. And this is where computer needs to say, what action would I take? So I am going to tell you in few slides, explain to you how you can do it using Monte Carlo simulation. This is a very, very popular technique that is used out there.

So the idea will be the following. You take your current state, and you just copy it into some other place. You copy it, and then you start doing simulations. So for instance, you can decide that now you want to irrigate land. You irrigated the land. You take some actions. You look for a few steps, and you observe how well do you do.

You can think about it like in chess. In chess, when we're doing simulations, you say, which one I'm going to move? OK, I'm going to move this piece. Then I'm going to try and see how the game would go. It's an obviously non-deterministic prediction because of his opponent, but you would say, OK, I play five moves, and they saw what happened.

And you record the state, and here you remember this is our vectors that I showed you in the very beginning, which records various information about the state and the action. It will tell you, you try to sort of match how the action maps to the state. It will tell how many terrains are there, what unit was moved during the state, and here, you say that if this is a state of the world and the actions that they took, I got some set and score. And then you try some other action, and you again record the vector.

And at the very end, you've decided what action are you going to take. But more interestingly, whenever you did use simulation, each time you observed how good they were. So now you're learning task is to predict how a particular situation maps to a score so that you know how to predict. Again, think about chess for those of you who are not familiar with Civilization. You just try to say in these particular circumstances, it's not good for me to take this move, because I'm going to get a lower score later. And the patterns that are good or bad are actually learned automatically by the machine when it does the simulations.

So now you've selected your next move, but next time when you are in state number 2, you already remember something about good and bad moves. So when you are trying all possible moves, you will use this knowledge to look at the right sample, because the space is so large you cannot allow to just randomly try stuff. So the knowledge that you gain through the simulation helps you to focus in the right part of the space. And you continue. This is a Monte Carlo session [INAUDIBLE].

So now you can ask yourself, OK, it plays. Why do I need text now? I do my simulation. The life is good. Why do we need to make the life more complex? So look at these particular examples that they started with whenever you need to have water to irrigate your crops. How this statistical model would learn this information? It needs to do lots and lots of simulation to make the right choice, and obviously, we're talking about the huge space. It may learn it, or it may not learn it. And obviously, you don't want it to take like three years to plan the next move, just trying exhaustively all the possibilities.

So the idea here is can I somehow incorporate this information into the simulation? Can I focus it into the right space within the simulations? And the way we are going to do it, we are now going to provide the machine-- in addition to the information about the state itself, we're going to provide the machine with an information from the manuals.

So machine now needs to find for each state what is the right sentence in the manual that we can use, and then for instance, use all the words from the sentence as features in our vector. You can say, but how does a machine know which sentence is a good one? It doesn't. But that's exactly where you're just learning this in the process. Sometimes it would select bad sentences, and it will get a bad feedback for that. And with time, it would learn to select better and better sentences.

Again, using the same type of thinking, you can say, maybe I just don't want to throw it all the words, because what I care about is the action that I want to take, and I want to know the attributes of the state. Again, using the same type of intuition, you can make the machine parse it into the different semantic categories and add these categories into your feature vector. And it learns using the same feedback mechanism.

So for those of you who are familiar with neural nets, this whole learning process actually is formalized as a neural net, which is multi-layered. When you start with the game-state [INAUDIBLE] and text, and at each level of the neural net, you make different analysis decisions. You select the sentence. You identify semantic pieces of the sentence, and eventually, you select the good move. And there are, again, formal mathematical methods to train those things that allow you to do it in a proper fashion. So let's see how it works. So before, I showed you the numbers. I will tell you how we evaluated the game. As the opponent in this game, we use AI game player. For those of us who don't play games, AI game play is something that the company shapes when it produces a game. It's a product that they develop, so when you buy your game, you can play against it.

And it's very well-engineered. It has a lot of knowledge and connections to all the parts of the game, so it's a very serious opponent. It should be good enough to play against a human. So the red part here is how the machine can play if it only uses Monte Carlo methods. Without any knowledge of the manual, you can see in this case, it loses to this AI opponent. It only wins 47% of the game against AI player.

However, if you add knowledge of the money all together with the Monte Carlo player, you can see that it actually beats, in most of the games, with 80% accuracy against the AI player. And again, it's very impressive, because AI player is something that has perfect knowledge and a lot of engineering strategies. We can clearly see that you can learn to behave if you read relevant material in a smart way.

And this is pretty much the end of my talk. I would just want to summarize the highlights of the approach, so we learn language by interacting with the world and observing the result. And what this approach enables is to pull together multiple sources of information to do language interpretation better.

And this direction we started just two years ago with my student, [? Brandon ?], who's here. There are lots and lots of things that we can do here, and I'm a firm believer that if we are successful, we would enable computers to actually act competently in the world with a lot of unstructured and [? imprinted ?] information. Thank you very much.

[APPLAUSE]

CHISOLM: We have time for a few quick questions.

AUDIENCE: I love to ask questions. That was very, very interesting. I have sort of two questions. One is I think I missed where the actual semantic labeling occurs. So the first question is, how does the system identify certain phrases in terms of their function? And the broader context-- the second question, which is really a broader context is one of the many hats I wear is that I work in assessment, and I'd love to understand more about how the SAT is scored using methods like this and, in particular, if they're Monte Carlo methods.

BARZILAY: OK. So let me just answer the first question. First, can you please bring my slides back? It's like when you put human in the loop, then it makes it harder. So the idea here is the semantic interpretations that we're talking about is relatively shallow semantic interpretation, where you just try to understand the action words or the action, which is like build city or irrigate and the attributes of the stage that are desirable.

And what happens here at each point, you can think about it as we did in the beginning. You sort of randomly guess what is the annotation? What is the semantic label of each phrase? And each phrase will have a lot of features. It will have syntactic information. You would have location. You would have lexical information.

And now for some particular labels that you put there, when you added them to the game and you observed the output, those would be positive outcomes. In some cases, you put your labels, and they happen to be very wrong, and you're going to get the negative outcome. And so this interaction process, you would be able to refine and correctly do this type of semantic tagging.

Now let me go to your second question about the annotation for SAT scoring. So it actually doesn't use this particular technique. It uses a technique which is maybe close to the positive and negative sentiment that I described. The way it is done, they have a huge database of essays, which are graded by humans.

And you can use a lot of linguistic representation from these essays and say, those are the features which are predictors of good essays, and those are the features which are predictors of bad essays. And you can use syntactic constructions, and people use some the way they're ordering information, a variety of things, and then you just train a very large model, and you do assessment in the end.

In many cases, it is difficult to get information with annotations. But they have these huge databases of millions of graded essays, so it wasn't a problem. And let me just say how it is used. So originally, these essays were graded by two humans, and when the humans disagreed, the [? set ?] human will read it, which is an expert. In this case, it's graded by one human and the machine, and when these two disagree, the human reads it. And they actually found out that the machine is much more consistent in scoring than the human readers. Yes.

AUDIENCE: Hi. I have one probably too silly and one too serious question. So the silly question is have you tested computer science students against the Civilization machine?

BARZILAY: Sorry. Can we--

AUDIENCE: Have you tested your Civilization player against the computer science students of MIT?

BARZILAY: We actually haven't. We haven't tried it against humans, no. We haven't.

AUDIENCE: What would you expect?

BARZILAY: I don't know. Actually now, and [INAUDIBLE], there is a website where humans actually can go and play against each other, and we are going to participate in this competition. And I would let you know how it goes. But if we make an analogy from other games like poker and others, we clearly see that for many games, machines for sure do better than humans. So I hope we can do better.

AUDIENCE: Good. So here's the serious question. Can we also teach machines to behave socially competent?

BARZILAY: So no. You can say that the general question is, what exactly does it mean? And if there is a way to properly formalize what does a socially appropriate behavior mean, maybe you can try to do it. But I think that if people-- this is not my area of expertise-- or people in MediaLab here who actually look at how to make robots social. And I think it's [INAUDIBLE] who does a lot of research. You may want to look at her papers.

CHISOLM: Thank you. I think we'll move on. Thank you, Regina.

[APPLAUSE]

So our next speaker is Peko Hosoi, who's associate professor of mechanical engineering, and she's the director of the Hatsopolous Microfluidics Lab. She has degrees in physics from Princeton and University of Chicago and a number of distinguished teaching awards. She's also a McVicar fellow and has been a Radcliffe Institute fellow and a Doherty assistant professor of ocean utilization. She studies the optimization of biological fluid systems for locomotion, and today is going to talk to us about small swimming lessons optimizing low Reynold's number of locomotion.

[APPLAUSE]

HOSOI: OK. Thanks, Penny, for that introduction, and thanks very much to the organizers for putting this workshop together. I have to confess that I've met most of the speakers in various capacities at MIT, but I've never heard any of them talk about their research. So I think this is a wonderful opportunity to sort of fill that gap. But swimming and optimization-- so today I'm going to talk to you about some of the challenges you face if you are very tiny and you live in a fluid environment.

So the first thing you need to know about systems like this is that-- let's see. How do I make this go? Do I have to point this somewhere? Yes? No? The first-- OK, you're only going to see my title slide. [INAUDIBLE]. Oh, did that go? This one?

CHISOLM: That's how you move the slide.

HOSOI: Oh, good. Oh, OK. Good. OK. I don't-- OK. I'll point over here. OK. So the first thing you need to know is that size matters in these systems. And most of you I think have an intuitive feel for this, because so, for example, if you look at a fluid system like this at a scale that you're used to dealing with on an everyday basis, you sort of know exactly what's going to happen in that system.

But if you compare that to something like what an ant would do, so an ant can actually go to a pool and drink, or it can pick up a drop of water and carry it around. So clearly the physics is different between the system on the right and the system in the middle there. And my slides are advancing in a funny way. So yes. Do I have to point this at something? Over here? OK, good. OK.

So clearly, the dominant physics in these situations is different, and in general, big things tend to be dominated by things like gravity or inertia, and small flows tend to be dominated by things like surface tension and viscosity. So the idea that I want you to take away in this talk is that because the physics is different at these different ends of the spectrum, you might expect that to be reflected in the behavior or in the morphology of biological systems that have to interact with these kinds of environments.

And, of course, I've cheated a little bit here, because big and small are relative terms. So I have to tell you what I mean by big and small, which will come up in the following slides. So I showed you a video on surface tension, so surface tension is what's dominating in that video with the ants. I'm now going to show you a video of what happens when viscosity is dominant in these systems.

So this video comes from the-- I am just not good with this pointer. Hello? This way? There we go. OK. Thanks. OK. So this video that I'm going to show you comes from the National Committee for Fluid Mechanics Films, and so many of you may not be aware that we have a National Committee for Fluid Mechanics Films, but we do. And because this is a celebration of the history of MIT, I think it's worth saying a few words about this.

This committee was actually founded by Asher Shapiro, who was faculty in the department of mechanical engineering, and it's a wonderful resource if you're looking for visualizations of fluid systems. It's also historically interesting, because all of the scientists in there look like they came out of a movie from the '50s.

But the fluid visualizations are incredible. So the movie I'm going to show you was actually not done by Asher Shapiro. It was done by another giant in the field of fluid mechanics, who is GI Taylor. And I'm pointing at the screen now. Like this? No. Oh, there. I'm pointing up there. OK. I'm still pointing. OK. GI Taylor. OK. Maybe I need to move over here.

So it's by GI Taylor, and he did the following experiment. So he said, all right, let's take a cylinder, two concentric cylinders. This is-- point at the screen? Hello? OK. Good. OK. So he used two concentric cylinders, and the idea is that he fills the gap between those cylinders with viscous fluid. And then what he's going to do is he's going to put a drop of dye in that gap, which you will see any minute now as soon as I get this pointer to work, and after the dye appears, he's going to slowly rotate the inner cylinder in order to mix that dye into the existing fluid.

So here's the video, which will also appear any minute now. There we go. So there's the cylinder. That's GI Taylor's hand you see, so this is the dye that he's putting into this small gap. So the small gap is filled with the viscous fluid now. And he's now going to spin the inner cylinder. In a minute, you'll see. So there's the dye. So there's the apparatus. He's now going to turn the handle, so he turns it slowly to mix the thing in. You can see it being mixed. There you go. There's one turn.

I think he turns it maybe three or four times, so you could get it sort of nicely mixed in. Three and four. And then just for good measures, he is now going to turn around and go the other way. So now he's going to turn this thing-- give it one turn this way, and go two. And you can see that as he comes around now-- so that was the third turnn-- as he comes around for the final turn, the dye actually unmixes.

So two messages to take away from that film. Number one is that when you change scales in fluid mechanics, you can no longer trust your intuition, because very strange things can happen. The second message to take away is that when viscous forces dominate, as they did in this system, the flows are reversible. They are time reversible, and this is something that you can show very easily by looking at the mathematical structure of the equations.

So this is a challenge if you're a tiny swimmer. So a tiny swimmer-- so now I'm going to tell you what I mean by a tiny swimmer. So a tiny swimmer-- I'm just going to hold this and hold the button down and point. So a tiny swimmer is defined-- when I say tiny swimmer, I'm defining it in terms of the Reynolds number, so the Reynolds numbers is a dimensionless number which tells you the relative effects of inertial and viscous forces.

So it can be defined as I've written up there. There are two parameters that are material parameters of the fluid, which is rho, the density of the fluid, and mu, the viscosity, but more importantly for our purposes, it also has the size of the organism and the swimming velocity of the organism. So you can see from this definition that if viscous forces dominate, the Reynolds number is going to be small, and then you're going to have these problems of reversibility that I just showed you. And one way to make the Reynolds number small is to make the size of your organism very tiny.

So to calibrate yourself, what do I mean by very tiny? So there's a person. So a person has a Reynolds number of about 10 to the fifth. So that does not count as tiny. If I move down, so for example, a tuna fish has a Reynolds number of about 10 to the sixth, because they're about the same size as a person, but they're better swimmers, so they have a better Reynolds number. Ducks are about 1,000. If you go down to the size of an ant, an ant has a Reynolds number of about 1.

So even an ant, you're not really down at small Reynolds number. You're not totally dominated by viscous effects. In order to be dominated by viscous effects, you have to move sort of over here. I don't know if I dare turn on another pointer, but OK. You have to move over here, so this is the region where you're at the size of about single cell organisms.

So this is the line where human vision cuts out, so beyond this, you can't really see without the aid of a microscope. And bacteria, this is roughly the smallest thing that you can see with a microscope. So the organisms that I'm going to be talking about in my talk live sort of in this region over here.

So before I tell you about the work we've actually done, I'm going to put up two slides on biology, and I am not a biologist. Let me put that caveat up front. And so the first slide I'm going to show you is a fluid dynamicist's view of biology. So here it is. This is a fluid dynamicist's view of biology. There it is. That's what it looks like to us. And there's two reasons why this is a fluid dynamicist's view of biology.

One is that we find it very confusing, and the second is that instead of organizing this by sort of traditional biological criteria, the person who drew this-- this was actually a famous image that was done by James [? Lightheel ?] in a lecture that he did in 1975. And you could tell this was done in the days before PowerPoint when you actually had to draw all your slides by hand.

So he's organized this not by any sort of biological criteria, but he's organized this by how things swim. And so if you look at the inner circle here, so everything in this inner circle to a physicist looks like a head, which is a sphere, with a flexible tail on it, where you might have n tails, and n is a small number-- usually 1, 2, or 3. So everything in that circle basically looks like that, a sphere with a tail.

And then the second thing he did is he now classified these into prokaryotic and eukaryotic cells. And that division comes over here. There's a green line up there, so the prokaryotic cells are up here, and the eukaryotic cells are down here. And again, for the purpose of this talk, what you need to know is that the swimming mechanisms are very different for both of those. And I'm going to focus on the eukaryotic cells, which live down here.

So that's my first slide on biology. My second slide on biology is to tell you something about the mechanisms that eukaryotic cells use to swim. And there's something that's sort of remarkable about these cells, and that is that if you look at the tails that they use to swim, they all have fundamentally the same structure. And the reason this is remarkable is if you think back to the biology you learned in high school, you remember that basically everything is a eukaryotic cell.

Prokaryotes are basically bacteria, and eukaryotes are basically everything else. And so if you look at the structure of the tails on these cells, which are flagella or cilia or something like that, they all have this thing that's called a 9 plus 2 microtubule structure, which looks like this. So there are a bunch of little tubules that surround a central pair of microtubules. and this doesn't matter if this is the cilia in your lung or the tail on a green algae or name your favorite eukaryote-- grasshoppers.

Everything has got this structure in it. And the remarkable thing about that is that that means that the diameter of all the tails are basically the same across all species. So when I say basically the same, I mean it's between 250 and 400 nanometers. So that's the first thing you need to know to understand what's going to come up in this talk.

The second thing you need to understand is that these tails are not passive structures. These tubules can slide relative to one another like this, and by doing that, they can induce a local bending moment in the tail. By inducing of a local bending moment, they can actually select the shape as a function of time. So those are the two things that you need to keep in mind as we go forward.

So here's the question that I want to ask. I want to know, can we use this information to predict morphology and kinematics of microorganisms from purely hydrodynamic considerations? And the basic idea here is that biological systems, we could hypothesize, have been optimized to perform certain tasks very well through millions of years of evolution. And so if we look at this structure of the hydrodynamical equations and look for optimal structures, do those structures then show up in biology?

So the first thing I'm going to do is actually I'm going to do kinematics, because that's a little bit easier. And then we'll come back to morphology, and optimizing kinematics looks something like this. So the first thing you want to do is you want to take a swimmer with a fixed geometry. So here's my swimmer-- for example, a swimmer with a fixed geometry. There you go. So that swimmer has a fixed number of limbs and a fixed way he can move his limbs around.

And you can say, all right, please actuate this swimmer for me in an optimal way. So you could choose to actuate this thing in any one of these possible ways. If you said, OK, I want to do something that is very efficient, you might say do something like this. If I want to do something that's very fast, you might do something like this.

And I'm now going to ask the same question for microorganisms. So I'm going to say, if you're given a fixed geometry that looks something like this, please tell me, how should you actuate this thing in order to do something that's most efficient or fastest or whatever it is you're trying to accomplish if you're this microorganism?

So let's see. So here's the model. I'm not going to go into the details of the model. I'm going to tell you that we started with the simplest structure that we saw in that big complicated diagram that I showed you that [? Lightheel ?] drew, where this is the organism. So it has a spherical head, and it has a single tail. And I'm just going to ask, what are the shapes that this tail should take in order to become an optimal swimmer?

And for those of you who are interested in the details, you can go and see how it works in this paper. But I'll just show you the answer. One of the remarkable things about this answer is it's incredibly robust. So no matter sort of what kind of crazy initial guess you give our algorithm, it will always converge to the same answer, which looks like that.

And so a couple of nice things about this solution is that A, it looks exactly like what you see in biological systems, exactly meaning-- I haven't said anything quantitative yet, but qualitatively, it looks pretty good. You always get a traveling wave solution. That wave is characterized by regions of high curvature that are connected by segments with low curvature, which is also what you see in biological solutions. If you actually do a kind of a quantitative comparison, there's a few things you can measure, and you do pretty darn well.

So for example, our computed ratio of amplitude to wavelength-- so there's the amplitude, there's the wavelength-- is 0.21. This is the best possible swimmer you could have. What you measure in biological systems about 0.20. If you look at the number of periods per tail, so that's sort of the number of wavelengths along here, the optimal thing you can do is 0.123. And the [? measurement ?] is a little bit bigger but still pretty close.

So we were pretty pleased with that. That seemed very promising. The problem with this is that kinematics is very difficult to measure in microorganisms. So we thought, OK, maybe we should go back, and we should look at something that's maybe a little harder to compute, but easier to measure. So let's move on and talk about optimizing morphology.