C. David Page- computer scientist

"Personally infinity is a pain for me."
(links for C. David Page)

Which importance do images have in your professional field?

images to display results of machine algorithms

The primary role that they play in my personal work, is just to display results of machine algorithms. For example if we learn a rule to predict what molecules will bind to a target proteine and be potential drugs, then we illustrate that rule by showing various molecules and how they fit the rule. I don’t work at all with analysing image data.

As I understood images in your discipline play also a role in analysing or structuring procedures.

the image plays a role in communicating a result to a human expert

Well, for me the image plays a role in communicating a result to a human expert. If the machine learning or data mining algorithm has analysed the data set and has recognized some regularities, like regularities in a set of molecules, then we communicate that rule verbally but also with a picture. So it’s a communication tool. Some people in my field do take image data as input and analyse image data. But I don’t work with image data.

I want to get to know more about the quality of the image you are communicating with. Do you use a classical picture or more an immaterial image?

molecular graphics: a traditional image with 3d ability

It is almost a classical picture except we often use molecular graphics software. So we can spin the molecule around and get a 3D effect from the 2D image, so the user can move the molecule around and see how the rule that was learned fits with the molecule. We may learn a rule that a molecule needs two negatively charged atoms and a positive charged atom in a certain geometric arrangement. We show the molecule with the 3 atoms highlighted in the use that we can spin the molecule around and see it from different perspectives. It’s a traditional image almost except for this ability to move it and get a 3-dimensional aspect.

Do you look different to images if they are computed?

just made to be an accurate depiction

The computed images would look much like a picture someone would draw except for this ability to move it around. But the image is not made to convey any feeling or emotion; it is just made to be an accurate depiction.

A new factor is that images are more and more web-based. How do you feel about web-based images?

web: giving many users in many places the same experience

I like web-based images. We are trying to implement a web interface for some of our software to give many users in many places the same experience that we have now. So users at other sites can run our machine learning software and have the same experience of moving the molecule around.

Mathematics plays an important role in your work. Do you still see mathematics in the result? Do you feel the math?

The images are mainly a way to help communicate the intuition of the mathematics.

Yes, the images are mainly a way to help communicate the intuition of the mathematics. The rule that we give back is mathematical, it will say something like a molecule bind to this target protein if it has two negative recharged atoms that are five angstroms apart from each other and a hydrophobic group - let’s say a carbon ring, that’s three angstroms from the first charged atom and four angstroms from the second charged atom. Mathematics is used to find the rule and also to communicate the rule and then the image illustrates the rule. So you can see the molecules, you can see the atoms and hydrophobic group in these distances that was specified in the rule. So there is a role of mathematics to the image.

For the non-mathematician it is always a wonder how you are working in mathematics and computer science with the factor infinity. How do you personally treat this factor infinity?

Personally infinity is a pain for me.

In my specific area of work infinity doesn’t come up very often except with regards to computerability. It turns out that sometimes, that when you add the rules, that we learn, to the background knowledge we have in logic, it can take infinitely long to answer some questions from the resulting theory. So we do it with infinity in that sense.
Personally infinity is a pain for me (laughing) because the cases where are run-time, where we can run into infinite run-times, this constitutes a problem. I prefer tasks where we can keep everything finite. If our run-time is finite, it is always the case that the datasets themselves are finite but they talk about finite quantities as well, molecules have a finite size, finite distances, so everything is bounded. Infinity usage just comes up to me in terms of run-time. I think infinity is a beautiful concept but for me it’s often a problem.

You talked today about that you worked with medicines analysing mammograms. I am sure you also did see the mammograms. How did you feel, what was your experience with this pictures?

wathing a mammogram:
"I felt confused."

I felt confused. When I see images like a mammogram, an x-ray or a sonogram, I can’t see what the physicians are talking about. Very often the physician said “here you can see the shape” and it doesn’t work quite that way to me. I know there is a use of training to see some shapes as interesting and other shapes as uninteresting and to be able to determine what they see in the image. Without that training the images just look very confusing to me. It’s frustrating to know that’s information there I cannot understand.

Because it’s not so discrete I suppose.

That’s right!

A string of bits can be interpreted as an image or as another type of media too. So it is not anymore so clear what an image is now. In economy you call this content. How do you feel about this concept?

Coming from my field, I like the idea that one interface can be interpreted in multiple ways.

I think it’s beautiful that some entities can be interpreted in multiple ways. For example in Gödel’s incompleteness theorem, he is able to encode a logical statement as a number. It’s that ability to have this entity be both a logical statement and a number. This makes it possible to come up with a startling mathematical result. The same thing comes up with Turings result, that haulting problem that it’s undecidable in general whether a Turing machine with a certain input will terminate, whether the computer program or basically run forever or terminate. Again he comes up with that result by equating a touring machine with a program, with a number and accessibility to interpret the same thing in several different ways that gives you the startling discovery. In general, coming from my field, I like the idea that one interface can be interpreted in multiple ways.
So it doesn’t bother me that this string of bits can be interpreted as an image and also as something else. I find it intriguing for example these results on protein music where you translate protein sequences into music: personally I don’t find all that aesthetically pleasing, but I think it is interesting that you can interpret the same string in multiple ways.

Do you meet in your job something like inner-images, imaginations?

Certainly imagination plays a very important role in my job and some of that imagination does involve creating mental images.

Do you have images in mathematics too?

Images help us in our creativity but we have to be careful as well.

Yes. We often use drawings to help us for example in creating a proof. We have to be very careful with an image because sometimes the images can lead us astray when we want to proof something about an algorithm. What’s tempting sometimes is to draw an image to represent a mathematical situation that we are interested in. But sometimes in drawing the image we make is too precise. We fill in details that are not in the preconditions for a proof and then the image may lead us into thinking there is proof of a theorem when the proof relies on extra details in the image, that are not in our assumptions for the proof. For example we might be trying to proof a theorem about something to that has to do with computation geometry. So we draw a certain type of shape, maybe it’s a theorem about polygons and so you draw a certain polygon and we see that the theorem result is true for that particular shape we just drew. But there may be some other shapes. So the shape has lead us thinking the result is always true. We draw an image but we maybe have to remember that it’s just one example of the case we are trying to consider. Images help us in our creativity but we have to be careful as well.

You talked about mathematical images as abstract pictures. Do you think that there is a close relation between abstract pictures and music?

I can imagine that there might be because almost any two entities are related if you think about long enough in some interesting way, but I don’t immediately see a relationship.

A very personal question to close our discussion: What is your favourite picture at home?


It’s a water colour that I bought for my wife. We lived for four years in England at Woodstock, not 8 miles from South Oxford. The picture shows a lovely street in Woodstock that we enjoyed walking down. There are some shops where we used to enjoy stopping in, seeing the shopkeeper. There is a church and we know that at the end of the street there is a palace and we used to go walking on the grounds. That’s my favorite.

interview from 2 February 2005 at Schloß Dagstuhl


Links for C. David Page:
C. David Page/ University of Wisconsin Departments of Computer Sciences, Madison 
C. David Page/ University of Wisconsin Departments of Biostatistics & Medical Informatics, Madison