This interview series seeks to introduce Fellows and students of Tembusu College to the wider community on a more personal level, and to create dialogue between these groups of people. This week, Professor Tay Yong Chiang shares with us his perspective on proof and truth, as well as his experiences interacting with his students both inside and outside the classroom.
Professor Tay received his BSc (Hons) in Mathematics from the University of Singapore, and a PhD in Applied Mathematics from Harvard University. At Harvard, he was a member of the Senior Common Room and, later, a Resident Tutor at Lowell House.
After graduation, he worked for a start-up called Sequioa that was building a parallel transaction processing machine. Life in industry was not very interesting, so he returned from Boston to join the National University of Singapore, where he is now a professor in the Departments of Mathematics and Computer Science.
What is a typical day for you like?
Typical day? There’s no typical day. It depends on what courses I’m teaching, it depends on what my graduate students are doing. So today I’m marking essays, and dealing with some requests from colleagues about papers and refereeing for conferences and journals. Sometimes I’m here, sometimes I’m back in the departments. It’s not a 9-to-5 job.
We heard you don’t look at other people’s papers before you write your own, so that you will be able to write with a broader scope. Would you like to tell us more about that?
So, first, you obviously have sources in my seminar group. Second, research is about generating new knowledge. Some people, when they train their students, what they do is they say “you go and read up on this topic and then find a new problem from what you’ve read”. So after they survey the literature, they find that “oh, this problem has not been solved”, “this problem has a solution”, or “the solution has certain weaknesses” etc. Then the student will now try to solve the unsolved problem or to improve on the current solution. To me, it’s a very incremental way of doing research. When doing research, one should have impact. Incremental research would never give you that kind of impact.
The way I do it, or the way I encourage my students to do it, is to not read up on the literature before they do it. Because you find that you are just going for those holes that are left open by other people, and that narrows your vision. If you don’t know what other people have done, you’re more likely to just attack it using your own perspective, your own intuition, etc. Then the chances are higher that you will come up with something entirely original. And after you have gotten your own idea and solution, then you can look at the literature and see how the literature relates to your solution. You will have a solution that is not constrained by what other people have done. To me, that’s more impactful.
Could you share with us what is your current area of research?
It’s called performance modelling for computer systems. So what I do is basically write equations to describe how computer systems behave. The question is, what is a computer system? A computer system could be the way memory is organised on a machine, and how the computer shuffles things in and out of memory when there are requests for memory space. So there are certain algorithms that determine the way they behave, and you can plot the data points on the graph. That would be a memory system. Another example of a computer system would be, say, wifi? If you have wifi here, your computer will talk to it. If you have one person, it behaves well, but if you have 40 people here talking to it, they start to get in each other’s way, so there are certain protocols to handle the congestion. My job would be to write equations that describe how this congestion behaves as the workload increases.
Just to give a more large-scale example, so now the hot thing is clouds and data centres. Data centres – in the case of Google, hundreds of thousands of machines are engineered to solve all kinds of problems. You do a Google search, it goes to one of these warehouses, and is split across all these machines. So the question is, how do they move things around when one machine fails, when they’ve got hundreds of thousands of machines and machines are failing all the time, and they have very tight constraints? You’ll notice that if you do a Google search, the answer comes back almost instantaneously. It’s actually not instantaneous, it’s like something within two hundred milliseconds. As long as it’s in that range, you will not perceive the delay. How can you engineer the machines and the software and the hardware centres so that the user does not perceive the delay? So that is a very big computer system and there are all kinds of performance issues there. One of the kinds of things that I do is analyse, for example, how they make use of the bandwidth, using equations.
With students from the Proof and Truth Junior Seminar
What were your intentions for starting a module on the topic of proof and truth?
When we signed on, we were expected to offer a seminar. It’s got to be a seminar that would appeal to different students from different faculties. My expertise is in computer science and mathematics. I think conceivably I could come up with a seminar having to do with computers, because computers touch every faculty. Whether you’re in law or medicine or arts or science, computers touch every discipline in some way. I’m not saying that law students use a computer to type an essay, no that’s not it. There’s a lot about intellectual property, for example, when it comes to the IT industry. So I could conceivably formulate a seminar based on that, but it would be kind of shallow, with very little depth to it. And I thought that for a seminar – “seminar” is a high-sounding word; a seminar is something you would imagine as a bunch of very nerdy guys, you know, discussing some very deep topics. I rather have a seminar that has more depth to it.
The other possibility would be to talk about mathematics. Not mathematics proper, but mathematics as a discipline. Before the university, the students’ experience of mathematics is actually calculation, but at the professional level, mathematics is very little calculation and more about proofs. So I thought it’d be good to have a seminar that talks about proofs, and besides, what is a proof? Proofs are about truth. Truth is a very ancient topic, with a lot of depth to it. So I think it is deserving, certainly, a worthwhile topic.
The first day of every seminar, I will show students the crest of Harvard University and Yale University. Do you know what is the commonality between the two? There’s the word “veritas” on it. “Veritas” is the Latin word for truth. It’s not unique to these two universities. You just do a search on various American universities, it’s very common to find the word “truth” in their mission statements. So it’s certainly something that many leading universities believe in – the search for truth, the respect for truth. I don’t think NUS has a mission statement, maybe it does, but it’s probably something bland, like you know, something about the world and something about Asia. So I think it’ll be good for freshmen to talk about proof and truth.
So the third part of the seminar is about the relationship between the two, and that’s where I bring in the mathematics. Not any deep mathematics, because I water it down so much. But Gödel’s theorem is one of the most important theorems in the last century, and we should talk about ground-breaking work, I think that’s fun.
If you look at all the Masters Teas, and the seminars etc in the college, they don’t talk about that kind of stuff. And that’s one of the ongoing issues that we have, that the seminars etc tend to be heavy on the humanities side and not so much on the technical side. Not a lot of seminars, not a lot of exhibitions etc about engineering or science or whatever. We used to have an interest group (IG) on that, formed by some physics students. But after they graduated, the IG just died. So I hope that at some point, we will have more and more engineering and science stuff going on in the college. We’re not there yet, it’s a work in progress.
With students during the Inaugural Tembusu Formal Dinner 2016
So would you say that that’s a reflection of students’ interests, or – how should we do this, should it come from the Fellows or should it come from the students?
Ideally it should come from the students instead of top-down, but the engineering students and the science students, right now, are not as proactive as the arts students, I guess. But that could just be historical reasons, since there are no prior experience and no role models to go on, whereas you have plenty of arts-related IGs.
Back to the module, it has had many iterations over the years. Has the seminar evolved, and if so, how?
I can’t remember all the iterations, but I do remember there was one class, some years ago, where there were two students who were very, very sharp. And when they start talking, I have to bring my best game, otherwise I get blindsided. So it depends on who is in the seminar, and it depends on how much effort they put in. Like those two students, they put in a lot of effort.
So I always emphasise to them at the beginning of the seminar, that – I know that in JS and SS, where you’re assigned readings, and you’ll read and come to class, and have some discussion – I don’t do that. I just say, no, go find out about “correspondence”, and they’re supposed to find out about it. Then last year one student commented that they didn’t have enough guidance, so this year, other than just “correspondence”, I gave them a set of key words to read up on. So that upped the game a bit, there’s a minimal bar to the quality of the discussion. And I think that’s what I should have been doing. So, over the years I’ve tweaked and tweaked the seminar. It doesn’t get easier, but I hope that it gets better and better.
We were wondering how your background as a mathematician and computer scientist also influences your thinking, especially regarding proof and truth?
In general, it matters a whole lot. I get very impatient with people when – for example, when people talk about politics or whatever, they can say things that they know are not true, and that really irritates me.
In the case of the seminar, there’s this famous theorem on Proof and Truth. I think it’s good for a non-mathematics student to understand what mathematics is about, and this particular theorem is a good exposure to that. Because professional mathematics is about proof, and this theorem is about what you can and cannot prove. For example, you can prove that you can’t prove something. So there’s a certain depth to it, it’s not just playing with words.
Do you always require everything to be logical or that ideas must follow a particular progression?
To require everything to be logical is to be unrealistic, because a lot of people behave non-logically, so I don’t expect other people to be completely logical, and I don’t expect myself to be completely logical either. I used to be very rational, and think through stuff when I make decisions, but there are many cases where I look at my rational choice and the alternative turns out in retrospect to be a better thing to do. So now I trust my instinct, my intuition, sometimes I feel like I should do this and I can’t rationally argue why I should do this, but I trust that there’s some other reason that I can’t figure out yet. Not everything can be figured out rationally, logically. Maybe there’s a logical explanation for it, it’s just that I haven’t figured it out yet, so I just go with my instinct.
What would you say is your perspective towards truth?
Perspective towards truth? It’s good to have the truth and know the truth, but a lot of times we don’t have it. I think one of the things the students get from this seminar is that there’s the truth, and there’s the model of the truth. And the model is all we have. We can try to be as accurate as possible, but we don’t know how accurate we are.
We’ve heard from some of your students that you have a very interesting fashion sense.
It’s just to entertain them. Otherwise it’s so boring.
Is it something you do constantly, or is it just for your students?
Usually for my students. Outside of my classes I don’t dress up.
Shan House members celebrating together during the Shan Christmas party
We see you talking to your students a lot in the dining hall, chatting with them, hanging out with them. We were wondering what drives your passion to have that close bond with them.
It’s actually part of the job. I think for the first couple of years, it was very painful. Every day, I dreaded going to dinner, because I will make myself sit with somebody I don’t know and talk to them. It’s only now that almost every time I go into the dining hall there is someone I can talk to, then the pain has gone away. I felt that that was what the college was supposed to do. I think the selling pitch was that you get to interact with professors and Fellows. But I don’t see that many of us in the dining hall. I think if we sell that line, we should deliver, and we should put ourselves in the dining hall and let the students talk to us. We don’t always talk about intellectual things. Every now and then it happens, but at least we should be accessible, and even though we might not be talking about something very deep, just being exposed to them breaks down the barriers, and sometimes you know who is who and what they do and everything, and some of this background information becomes critical at times. And anyway, it’s fun talking to them.
Has being in Tembusu impacted or changed you in any way?
I think being in constant contact with people and students makes a whole lot of difference to me. For a long while, I was basically alone, except when I’m in class. So I noticed it was affecting me psychologically. You know, it’s very unhealthy to always be talking to yourself. But now, on a daily basis, throughout the day, as part of the job and everything, I have to talk to people, and I think it’s way more healthy, for me personally. If you are too solitary, I think it’s not a good thing.
We found out from a friend that there is a Shan House pledge. And there’s a very interesting line that says, “I will always support and defend Prof Tay.” What are your thoughts on your House, and how has being a Residential Fellow been for you?
First of all, that line was not put there by me. (laughs) It was done by the first House Captain, Jonathan Ong. When they came up with the creed, I was actually away on some conference trip. And when I came back, I found out they have done this thing, I was like “okay”. They were just having fun.
Anyway, there are two aspects to the House. One is the logistics aspect to it, how to form the House Committee, how to go about electing a House Captain and all that. I think by now we are more or less stabilised. And there’s the day-to-day running of the House, like what are the roles of the Residential Fellow compared to Graduate Fellow, etc. I think we’ve worked out of the details of the mode of operations for that.
The other aspect of it is – I don’t know how to call it, the House culture, or the experience – what should the experience be like, and how to go about fostering it. That one I can’t say that we are there yet, and I’m not sure if we will ever be there, because two years is not a long time. So it’s kind of unstable. I imagine that it could be that some years the House is really bonded, and some years it’s kind of loose. I think that can happen, but every year, we try. If we see that it is loose, we try things so that we can bond them better. So that one is an ongoing exercise.
So would you say that, over the years, the House has moved closer to what you expected?
The first couple of years, I had no clue of what I was supposed to do. By now I have a better feel for the dynamics. So it’s closer to how I want it to be. For a while – so, I don’t have a Smart phone, I only have a stupid Nokia. So I’m not part of Whatsapp, I’m not a part of any chat group or anything. For a long time, I didn’t know what was going on upstairs. Until recently, they told me that I could use Telegram on my laptop, so now I can hear their chatter that is going on upstairs throughout the day, and it’s kind of – have you guys ever watched The Waltons? It’s a soap opera, a very long-running soap opera, but anyway, it kind of reminds me of The Waltons, which is this family with a lot of children and they are always squabbling and chattering and everything. And I look at Telegram, and it’s kind of like that, you know. Throughout the day, you hear this chatter. And to me, it’s kind of warm. There is like a group of brothers and sisters just teasing each other and fooling around, and I think as long as we can generate and maintain a warm and cosy and homely atmosphere in the House, I think we’ll be okay.
Shan House sharing a meal together after Inter-House Games this year
Could you tell us about your most memorable experience interacting with your students?
There was one semester where I went on leave, a sabbatical, and then when I came back, it was, I think, during the reading period or during the exam period, and my House held a party for me. A lot of people showed up, and that felt very good because everyone was busy, they had to prepare for the exam and everything. That was in the first semester, when something like half the House did not know who I am, because they were year ones. But still they showed up for the party. I felt good about that, it was very warming. So I must have done something right, if the year ones, despite not knowing me, the seniors must have told them lies to make them show up. (laughs)
This interview was conducted by Denise Goh and Jerrell Seah, with images contributed by Prof Tay, Yeo Guek Ling, Caroline Djati Utomo, Ng Jing Rou, Tay Ying Hui and tStudios.