The great reformulation of algebraic geometry

“Tate helped shape the great reformulation of arithmetic and geometry which has taken place since the 1950’s.” — Andrew Wiles

At the Heidelberg Laureate Forum I has a chance to interview John Tate. In his remarks below, Tate briefly comments on his early work on number theory and cohomology. Most of the post consists of his comments on the work of Alexander Grothendieck.

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JT: My first significant work after my thesis was to determine the cohomology groups of class field theory. The creators of the theory, including my thesis advisor Emil Artin, didn’t think in terms of cohomology, but their work could be interpreted as finding the cohomology groups H0, H1, and H2.

I was invited to give a series of three talks at MIT on class field theory. I’d been at a party, and I came home and thought about what I’d talk about. And I got this great idea: I realized I could say what all the higher groups are. In a sense it was a disappointing answer, though it didn’t occur to me then, that there’s nothing new in them; they were determined by the great work that had already been done. For that I got the Cole prize in number theory.

Later when I gave a talk on this work people would say “This is number theory?!” because it was all about cohomology groups.

JC: Can you explain what the great reformulation was that Andrew Wiles spoke of? Was it this greater emphasis on cohomology?

JT: Well, in the class field theory situation it would have been. And there I played a relatively minor part. The big reformulation of algebraic geometry was done by Grothendieck, the theory of schemes. That was really such a great thing, that unified number theory and algebraic geometry. Before Grothendieck, going between characteristic 0, finite characteristic 2, 3, etc. was a mess.

Grothendieck’s system just gave the right framework. We now speak of arithmetic algebraic geometry, which means studying problems in number theory by using your geometric intuition. The perfect background for that is the theory of schemes. ….

Grothendieck ideas [about sheaves] were so simple. People had looked at such things in particular cases: Dedekind rings, Noetherian rings, Krull rings, …. Grothendieck said take any ring. … He just had an instinct for the right degree of generality. Some people make things too general, and they’re not of any use. But he just had an instinct to put whatever theory he thought about in the most general setting that was still useful. Not generalization for generalization’s sake but the right generalization. He was unbelievable.

He started schemes about the time I got serious about algebraic geometry, as opposed to number theory. But the algebraic geometers classically had affine varieties, projective varieties, … It seemed kinda weird to me. But with schemes you had a category, and that immediately appealed to me. In the classical algebraic geometry there are all these birational maps, or rational maps, and they’re not defined everywhere because they have singularities. All of that was cleared up immediately from the outset with schemes. ….

There’s a classical algebraic geometer at Harvard, Joe Harris, who works mostly over the complex numbers. I asked him whether Grothendieck made much of a difference in the classical case — I knew for number theorists he had made a tremendous difference — and Joe Harris said yes indeed. It was a revolution for classical algebraic geometry too.

Writing down an unwritten language

In this post I interview Greg Greenlaw, a friend of mine who served as a missionary to the Nakui tribe in Papua New Guinea and developed their writing system. (Nakui is pronounced like “knock we.”)

JC: When you went to PNG to learn Nakui was there any writing system?

GG: No, they had no way of writing words or numbers. They had names for only seven numbers — that was the extent of their counting system — but they could coordinate meetings more than a few days future by tying an equal number of knots in two vines. Each party would take a vine with them and loosen a knot each morning until they counted down to the appointed time — like and advent calendar, but without numbers!

JC: I believe you said that Nakui has a similar grammar to other languages in PNG but completely different vocabulary. Were you able to benefit from any other translation work in the area? Will your work serve as a starting point for translating another language?

GG: Yes. Missionaries had moved into our general area back in the 80’s and the languages they studied had mostly the same grammar features that we saw in the Nakui language. This sped the process, but in truth, the slowest part of learning to speak was not analyzing the grammar, it was training yourself to use it. Each Nakui verb could conjugate 300 different ways depending on person, recipient, tense, aspect, direction, and number.

JC: Do any of the Nakui speak a pidgin or any other language that served as a bridge for you to learn their language?

GG: We were blessed with one very good pidgin speaker when we moved into the village and several others who spoke the Melanesian Tok Pisin at a moderate level. That was a help in eliciting phrases and getting correction, but there were limits to how much they understood about their own speech. They had never thought about their language analytically and could not state a reason for the different suffixes used in the language, they just knew it was the right way to say something. Most peculiar was that they couldn’t even tell where certain word breaks were. Their language had never been “visible” to them. Nouns were easy to separate out, but it was hard to know if certain modifiers were affixes or separate function words.

JC: What are a few things that English speakers would find surprising about the language?

GG: Nakui has very few adjectives but innumerable verbs. They do the majority of their describing by using a very specific verb. There is a different verb for cutting something in the middle as opposed to cutting off a small section or cutting it long ways or cutting something to fall downward or cutting something to bits. The correct verb for the situation will also depend on the object being cut — is it log-like, leaf-like, or flesh-like.

JC: Do you try to learn a new language aurally first before starting on a writing system, or do you start developing a writing system early on so you can take notes?

GG: It’s language, so you always want your ears and tongue to lead your eyes. We use the international phonetic alphabet to write down notes, but we encourage language learners to hold off on writing anything for almost of month. After they are memorizing and pronouncing correctly a host of nouns and some noun modifiers, then we encourage them to start writing down their data with the phonetic alphabet. About half way to fluency they usually have enough perspective on the variety of sounds and where those sounds occur that they can narrow down a useful alphabet.

JC: How long did it take to learn the language? To create the writing system? How many people were working on the project?

GG: Primarily Tim Askew and myself, but there were three other missionaries that worked among the Nakui in the early days and each had some contribution to our understanding. The biggest credit really belongs to God, by whose grace we were allowed to live there and by whose strength we were able to chip away for three years until the job was done.

JC: Can you describe the process you went through to create the writing system?

GG: Well after collecting thousands of words written phonetically we could start a process of regularizing all that data. Looking at the language as a whole we had to decided the sleekest, most uniform way to consistently spell those sounds phonetically. After cleaning up our data we could take a hard look at which of the sounds were unique and which are just modified by surrounding sounds. Phonetically the English language has three different ‘t’ sounds: an aspirated ‘t’, and unaspirated ‘t’, and an unreleased ‘t’. We only think of one ‘t’ sound, though, and it would be confusing (and irritating) if we had three ‘t’ symbols in our alphabet. Our ‘t’s just become unreleased automatically when they are at the end of a word and they become unaspirated when they blend with an ‘s’. You need to narrow down the number of sounds to just the ones that are significant and meaningful. It is only those unique sounds that are given letters in the alphabet.

JC: What is the alphabet you settled on? Do the letters represent sounds similar to what an English speaker would expect?

GG: We found 10 vowel sounds and 10 consonant sounds were needful in the Nakui language. The 10 consonants are symbolized the same as English, but the vowels had to be augmented. We borrowed the letter ‘v’ to become the short ‘u’ sound and used accent marks over other vowels to show their lowered and more nasalized quality.

JC: Could you give an example of something written in Nakui?

GG: This is John 3:16. Músvilv Sisasvyv me iyemvi, “Kotvlv asini niyanú nonú mvli mvlei ufau. Múmvimvilv, tuwani aluwalv siyv tuwayv itii, asinosv. Mvimeni notalv me svmvleliyelv, ‘Sisasvni yáfu kokuimvisv,’ múmeni nonv ba itinvini, i tínonvminvini.

JC: Is it unusual for a language to have as many vowel symbols as consonant symbols?

GG: Good question. I’m not sure what normal would be worldwide, but I know we have a lot more than five vowel sounds in English! All our English vowel symbols have double or triple allophones (long sounds, short sounds, alternate sounds) making it very challenging to instruct my 6 yr old in the skill of reading.

JC: Have you published anything on your work, say in a linguistics journal?

GG: No, there is nothing unique in what we did. Truth is, we organized our findings and reported our work in an informal, non-academic, pragmatic way because our goal was not a PhD in anthropology, but a redeeming ministry in the lives of tribal men and women and ultimately a commendation from the Maker of men.

JC: How many of the Nakui can read their language?

GG: All the young men in our village are readers now, with the exception of a dyslexic man who attempted our literacy course three times without result. About 1/3 of the young women can read. They have less available time for study, and in the early days the village leaders did not allow the girl to be in class with the boys. As a result, literacy for ladies had a slower start and fewer participants. There were older men who tried to learn to read, but none that succeeded. The gray matter seemed to have stiffened.

JC: If English didn’t have a writing system and you were designing one from scratch, what would you do differently?

GG: Wow, we have six kids we’ve taught to read – we would do a lot differently! The ideal is to have one symbol for each meaningful sound in the language. English would need more vowels and fewer consonants. Life would actually be more pleasant without ‘c’, ‘j’, ‘q’ and ‘x’. If you removed those and added about six vowels we could come up with a spelling system that was predictable and easy to learn.

JC: Anything else you’d like to say?

GG: One of the most remarkable things about the Nakui language is how sophisticated and complex it is. Unblended with other languages, it is extremely consistent in its grammar. Although it is in a constant state of change (rapid change relative to written languages of the world), it remains organized. This order is not to the credit of the society that speaks it, it happens utterly in spite of them. They are completely unaware of the structure of their own grammar and are perhaps the most disorderly people on the planet. The aspects of life over which they hold sway are corrupt and miserable, but in this small, unmanaged area of their lives, a glimpse of the divine still peeks out. The God of order, who created them in His own image, gave them an innate ability to communicate complex ideas in and orderly way. Like Greek, they specify singular, dual and plural. They have six tenses (English has only three), and 11 personal pronouns (English has only six). Every verb is conjugated to carry this specificity with extreme consistency. The verb to ‘go’ is the only irregular verb in the whole Nakui language. English, although vast, is a disheveled mess compared to what is spoken by these stone age people in the swamps of interior New Guinea.

Related posts:

Interview with Sir Michael Atiyah

Yesterday I had the privilege of interviewing Sir Michael Atiyah. We talked about mathematical writing, the interplay of abstraction and application, and unified theories of physics. A shorter excerpt, focusing on mathematical exposition, will be appears on the HLF conference blog.

Update: I’ve posted the audio of the interview here.

JC: I ran across your expository papers when I was a student and very much enjoyed reading them. Two things stood out that I still remember. One was your comment about one-handed pottery, that the person creating it might be very proud of what he was able to do with only one hand, but the user of the pottery doesn’t care.

MA: That was my response to the kind of highly technical mathematics that showed you could do something under extremely minimal hypotheses, but who cares? Sometimes its useful, but often its for the benefit of the technicians and not the general user.

JC: The other thing I remember from your papers was your rule that exposition should proceed from the particular to the abstract.

MA: I have strong views on that. Too many people write papers that are very abstract and at the end they may give some examples. It should be the other way around. You should start with understanding the interesting examples and build up to explain what the general phenomena are. This was you progress from initial understanding to more understanding. This is both for expository purposes and for mathematical purposes. It should always guide you.

When someone tells me a general theorem I say that I want an example that is both simple and significant. It’s very easy to give simple examples that are not very interesting or interesting examples that are very difficult. If there isn’t a simple, interesting case, forget it.

One feature of mathematics is its abstraction. You can encompass many things under one heading. We talk about waves. For us a wave is not a water wave, it’s an oscillating function. It’s a very useful concept to extract things out.

Mathematics is built on abstractions. On the other hand, we have to have concrete realizations of them. Your brain has to operate on two levels. It has to have abstract hierarchies, but it also has to have concrete steps you can put your feet on.

Everything useful in mathematics has been devised for a purpose. Even if you don’t know it, the guy who did it first, he knew what he was doing. Banach didn’t just develop Banach spaces for the sake of it. He wanted to put many spaces under one heading. Without knowing the examples, the whole thing is pointless. It is a mistake to focus on the techniques without constantly, not only at the beginning, knowing what the good examples are, where they came from, why they’re done. The abstractions and the examples have to go hand in hand.

You can’t just do particularity. You can’t just pile one theorem on top of another and call it mathematics. You have to have some architecture, some structure. Poincaré said science is not just a collection of facts any more than a house is a collection of bricks. You have to put it together the right way. You can’t just list 101 theorems and say this is mathematics. That is not mathematics. That is categorization. Mathematics is not a dictionary.

JC: I think someone called that stamp collecting or bug collecting.

MA: Yes. Rutherford was very scathing about chemistry. He said there is Schrodinger’s equation, and everything else was cookery.

JC: I think people are more willing to give these examples verbally than in print.

MA: You’re quite right. It is kind of a reaction in recent times. People began to go beyond what they could prove and got a bit woolly and they got a bad reputation, like some of the Italian algebraic geometers. So you are taught to be rigorous, and you learn to be very, very rigorous. And then you think that your papers have to be ultra-rigorous, otherwise the guys behind you will find fault with what you’re saying. The need for rigor, it’s a bit like the people who are afraid of being sued by the lawyers. If you don’t put it down, 100%, someone will sue you! People cover themselves in advance, but the result is an unreadable paper.

But when you talk like this, you’re allowed to lower the level of rigor in order to increase the power of explanation. You can explain things using hand waving, use analogies, leaving out technical details, because you want to get the idea across. But when people write, particularly mathematics, and particularly in the last decades of the last century, people became very formalistic. Papers were reject if they were not rigorous enough. People were reacting to the loose talk of the past. So we went to the other extreme. And most papers aren’t read. That’s a theorem! Someone said the average number of readers of a paper is one, and that’s the author.

JC: And with multiple authors, maybe it’s a fraction.

MA: That’s right. I used to tell people, make your introduction understandable to a general mathematician. Don’t get into the technicalities there. Say you’ll deal with them later. Don’t just say “Let X be a space” and jump into the details but that’s what people do. So you’re right. But people know when they give a lecture to behave differently, they can use all the tools of hand-waving, literally! [waves hands], to get idea across.

Some people write so well it’s as good as a lecture. Hermann Weyl is my great model. He used to write beautiful literature. Reading it was a joy because he put a lot of thought into it. Hermann Weyl wrote a book called The Classical Groups, very famous book, and at the same time a book appeared by Chevalley called Lie Groups. Chevalley’s book was compact, all the theorems are there, very precise, Bourbaki-style definitions. If you want to learn about it, it’s all there. Hermann Weyl’s book was the other way around. It is discursive, expansive, it’s a bigger book, it tells you much more than need to know. It’s the kind of book you read ten times. Chevalley’s book you read once. You go back to these other books. They’re full of throw-away lines, insights that are not fully relevant for going from A to B. He’s trying to give you a vision for C. Not many people write like that. He was an exception.

In the introduction he explains that he’s German, he’s writing in a foreign language, he apologizes saying he is writing in a language that was “not sung by the gods at my cradle.” You can’t get any more poetic than that. I’m a great admirer of his style, of his exposition and his mathematics. They go together.

JC: I ran across an old paper by Halmos recently where he refers to your index theorem as a pinnacle of abstraction, and I thought about the comparison with Shinichi Mochizuki’s claimed proof of the abc conjecture. The index theorem rests on a large number of abstractions, yet these are widely shared abstractions. Mochizuki’s proof also sits on top of many abstractions, but nobody understands it.

MA: These problems have a long history. The past is part of your common heritage. They generalize classical theorems. They go step by step through abstractions. Everybody knows what they’re for. So there’s a big pyramid. The base is very firm. The purpose of abstraction is that you can go back down to earth and apply it here or apply it there. You don’t just disappear in the clouds. You walk along the ridge and go down to this valley or that.

JC: Maybe the proof of the abc conjecture is more of a flag pole than a pyramid.

MA: And when you get to the top of a flag pole, what do you do? You could be like the hermit saints who would sit on a pillar. …

JC: I saw a video recently of a talk you gave a couple years ago in which you described yourself as a “mystic,” someone hoping for a unification of several diverse theories of physics.

MA: That’s right. I was saying that there are these different schools of thought, each with a prophet leading them. I wanted to say that I didn’t follow any one of them, that you can search for the truth through many different ways. The mystic thinks there’s a little bit of truth in everybody’s line. I think every interesting line has something to be said for it.

There are the string theorists, that’s the biggest school, and people like Roger Penrose, Alain Connes, … They all have strong ideas, and they attract a certain group of followers. These are serious people, there’s serious reason to believe what they’re doing, and there’s something in it. Bridges have been built between these theories. They’ve found unexpected links between them. So that’s already a bit of convergence. So I’m hoping there will be more convergence, using the best of each theory.

It would be sad if we’ve seen the last of the visions of the prophets. It would be sad if new fundamental insights were no more. There’s no reason it should stop. At the end of the 19th century people thought physics was finished. We know absolutely everything, but at the beginning of the 20th century it exploded. There’s no reason not to think there will be further revolutionary ideas emerging. Any day, any time, anywhere.

I’m an optimist. I believe in new ideas, in progress. It’s faith. I’ve recently been thinking about faith. If you’re a religious person, which I’m not, you believe God created the universe. That’s why it works, and you’re trying to understand God’s works. There are many scientists who work in that framework. Scientists, outside of religion, have their own faith. They believe the universe is rational. They’re trying to find the laws of nature. But why are there laws? That’s the article of faith for scientists. It’s not rational. It’s useful. It’s practical. There’s evidence in its favor: the sun does rise every day. But nevertheless, at the end of the day, it’s an article of faith.

I gave a talk about Pythagoras. Bertrand Russell said that Pythagoras was probably the most influential philosopher who ever existed, because he was the first person to emphasize two things, the role of numbers in general, and the role of numbers in music in particular. He was so struck by this that he believed number were the base of the universe. He was the first person to articulate the view that the universe is rational, built on rational principles.

JC: What do you think of category theory? Do you think it plays a role in this grand unification?

MA: Well, I’m a conservative in many ways. As you get older you get more conservative. And I don’t believe in things unless I’m convinced of their utility. Ordinary categories are a useful language. But it’s become now more formal. There are things called 2-categories, 3-categories, building categories on categories. I’m now partially converted. I think it may be necessary. Algebra was an abstraction when it first came along. Then you get into categories and higher levels of abstraction. So I’m broad minded about it, but I’d like to be persuaded.

Interview with Sacha Chua

I spoke with with Sacha Chua last week. We talked about entrepreneurship, Emacs, having eclectic interests, delegation, and more.

Navigation cons from Sacha's blog

J: I ran into you by searching on Emacs topics. When I look at your blog, I see that you do a lot of interesting things, but it’s a little hard to get a handle on exactly what you do.

S: Oh, the dreaded networking quirky question. What exactly do you do?

J: Yeah, people have said the same thing to me. Not to put you in a box, but I was curious. I see from your site that you do graphic art — sketching and such — and it doesn’t create the impression that you’re someone who would spend a lot of time in front of Emacs. So I’m curious how these things fit together, how you got started using Emacs and how you use it now.

Image by Sacha Chua

S: So my background is actually fairly technical. I’ve been doing computer programming for ages and ages. In high school I came across a book Unix Power Tools, which is how I got interested in Emacs. And because I was interested in programming, in open source, a little bit of wearable computing as well, I got to know Emacs and all these different modules it had. For example, Emacspeak is amazing! It’s been around since the 1990s and it’s a great way to use the computer while you’re walking around. Because I love programming and because I wanted to find a way to help out, I ended up maintaining PlannerMode and later EmacsWiki mode as well.

When I went to university, I took up computer science. After I finished, I taught. Then I took my masters in Toronto, where I am now. Emacs was super helpful — being able to do everything in one place. After I finished my masters, I did a lot of software consulting with IBM. I did business consulting as well. Then in 2012, after saving up, I decided to go on pretty much the same adventure you’re on. I’m completely unhirable for the next five years! Most businesses struggle for the first five years, so I saved up enough to not worry too much about my expenses for the next five years. I’m one year in, four years to go, and that’s where I am.

At networking events, I like to shake people up a bit by telling them I’m semi-retired. I’m in this five-year experiment to see how awesome life can be and what I can do to make things better. I’ve done technical consulting, business consulting, sketching, illustration, writing, all sorts of things. Basically, my job description is context-dependent.

J: I understand that.

S: I use Emacs across all the things I do. When I’m doing technical and business consulting, I use Emacs to edit code, to draft documents, even to outline comic strips. And when I’m doing illustration, Emacs — especially Org Mode — helps me keep track of clients and deliverables, things to do, agenda, calendar, deadlines.

J: I’m basically running my life through Org Mode right now. When you say you use Emacs to draft documents, are you using LaTeX?

S: I used LaTeX when I was working on my master’s thesis and other papers, I think. Now I mostly use org mode and export from there.

J: Are you using Emacs for email?

S: I used to. But I’m stuck on Windows to use drawing programs like Sketchbook Pro on my Tablet PC. So it’s harder to set up my email like I had it set up when I used Ubuntu. Back when I used Ubuntu, I was very happy with Gnus.

J: Do you work entirely on Windows, or do you go back and forth between operating systems?

S: I have a private server that runs Linux. On Windows I run Cygwin, but I miss some of the conveniences I had when I had a nicely set-up Linux installation.

J: When you’re running Emacs on Windows, I’m sure you run into things that don’t quite work. What do you do about that?

S: Most things work OK if they’re just Emacs Lisp, but some things call a shell command or use some library that hasn’t been ported over yet. Then I basically wail and gnash my teeth. Sometimes I get things working by using Cygwin, but sometimes it’s a bit of a mess. I don’t use Emacs under Cygwin because I prefer how it works natively. I don’t run into much that doesn’t work.

J: So what programming languages do you use when you’re writing code?

S: I do a lot of quick-and-dirty things in Emacs Lisp. When I need to do some XML parsing or web development, I’ll use Ruby because a lot of people can read it and there are a lot of useful gems. Sometimes I’ll do some miscellaneous things in Perl.

I love doing programming and putting together tools. And I quite enjoy drawing, helping people with presentation and design. So this is left brain plus right brain.

It does boggle people that you can have more than one passion, but others are, like, “Yeah, I know, I’m like that too.”

J: I think having an interest in multiple things is a healthier lifestyle, but it’s a little harder to market.

S: Actually, no. I finally figured out a name for my company, ExperiVis, after a year of playing with it. People reach out to me and we figure out whether it’s a good fit. I don’t need to necessarily guide people to just this aspect or another of my work. I like the fact that people bump into these different things.

J: When we scheduled this call, I went through your virtual assistant. How do you use a virtual assistant?

S: One of the things I don’t like to do is scheduling. I used to get stressed out about scheduling when I did it myself. I’ve always been interested in delegating and taking advantage of what other people enjoy and are good at. I work with an assistant — Criselda. She lives in the Philippines. I found her on oDesk. She works one to four hours a week, more or less, and keeps track of her time.

J: What else might you ask a VA to do?

S: I’ve asked people to do web research. I’ve had someone do a little bit of illustration for me. I’ve had someone do a little bit of programming for me because I want to learn how to delegate technical tasks. He does some Rails prototyping for me. I have someone doing data entry and transcription. It’s fascinating to see how you can swap money for time, especially for things that stress me out, or bore me, or things I can’t do.

Every week I go over my task list with my VA to see which of the tasks I should have delegated. Still working on it!

***

Later on in the conversation Sacha asked about my new career and had this gem of advice:

Treating this as a grand experiment makes it much easier for me to try different approaches and not be so scared, to not treat it as a personal rejection if something doesn’t work.

Related posts:

People I’ve interviewed and people who have interviewed me

Interview with Michael Hammel, author of The Artist’s Guide to GIMP

Michael J. Hammel is the author of The Artist’s Guide to GIMP, a book I reviewed three weeks ago. The following interview is based on my correspondence with Michael.

JC: The bio on your book says that you are an embedded software developer. Is GIMP something you use for fun or is it related to your work? Was it related to your work before?

MH: I use it once in awhile at work but not often. GIMP started as something related to what I worked on when it first came out (graphics software for Unix systems). But I’ve never been paid to be an artist. At one point I looked at trying to use what I knew about it to leverage my way into Pixar or Dreamworks. But that never panned out and my interest in that kind of animation has peeked and ebbed, mostly because I decided I didn’t want to live in California (too expensive).

JC: How did you become involved in the development of GIMP?

MH: When GIMP was born, back around 1995 or so, I was working for a company that provided commercial X servers for Unix systems (Xi Graphics, started by Thomas Roell who wrote the original reference implementation of an X server for 386 systems, aka X386, which begot XFree86 which begot X.org). I packaged Motif as part of my work. A guy I worked with noticed GIMP’s Motif version and pointed me at it. I wrote a plugin for John Beale’s sparkle code (the original Sparkle plugin). I’ve been working with GIMP ever since.

JC: Are you still a developer for GIMP or primarily a user?

MH: A user. I haven’t provided any useful code development to the project in quite sometime.

JC: What’s it like to be a developer on GIMP?

MH: Take this with a grain of salt. It’s a follower’s view from the outside, without being involved with the developers directly.

GIMP’s developer community is somewhat different than other open source communities that I’ve been involved with. GIMP’s leadership is de facto, but not necessarily structured. Many other projects have defined leaders with defined tasks. GIMP’s development is a little more oriented towards scratching your own itch: pick something that that you want to improve and start working on it. The only tough part (at least for some) is understanding and adhering to the main developers coding styles and rules, which are not (to my knowledge) written down.

My only complaint with this style is it tends to allow long term development cycles. End users can’t rely on when new features might be available. While the developers want do things “the right way”, that means that users have been waiting a very long time, for example, for deep paint support. There is a tradeoff for how you do development. Remember that the developers are volunteers, so there is no valid reason for complaining if you, as a user, aren’t getting what you want when you want it. If it bothers you, step in and help out. Otherwise, do as I do: be content with their development process.

JC: What advice would you give people who want to learn image editing?

MH: I learned how to use GIMP by reading Photoshop texts. Image editing is a common set of processes. Think about what you want to do if you weren’t using software. You’re house needs a new color? You mask off the window boarders and roof line and start painting. Same thing in image editing. Only difference: it’s easier to try different colors. Image editing is all about selections and masks. I’m not talking about creating the next Marvel comic, I mean editing existing images. Once you identify what needs to be changed using a selection and mask, you can do all kinds of things: copy and distort, recolor, refocus, etc.

Making comics or custom drawings requires real artistic talent to create a rough design on paper, then import (via scanner or digital camera) into GIMP for cleanup and coloring.

Personally, I prefer taking photos and mixing them together to create a scene that otherwise wouldn’t exist. There is a small example of this in the book. A photo of a city skyline as it exists and a munged version I created to make the city look decayed and falling apart. Beats me what people think of that image, but the creative process that went into it was very relaxing.

JC: What advice would you give people who want to learn GIMP in particular?

MH: Buy my book. Seriously. You learn both at the same time: what is image editing and how do you do it with GIMP. GIMP is just like any other desktop software. You learn where the menus are and what the various windows provide. The rest of your time is learning process — creating a workflow to produce a specific image type or style.

JC: What other software do you use/recommend for creating graphics?

MH: I use simple viewers like Geeqie for browsing images, but if you’re into photography you’ll nee something like f-spot. Photographers, who are nuts about image quality, should learn ufraw. Those interested in 3D or animation should take a look at Blender.

JC: Do you want to say anything about your work with embedded development?

MH: It’s my primary focus in life these days. I’m working on creating a custom media-focused Linux distribution (which I call BeagleBox) for the BeagleBoard C4 (and later the xm). I’d like to get my hands on the Raspberry Pi but wasn’t able to place an order when they first went on sale.

Embedded work is the future for Linux. The desktop for non-techies might change to tablets or such, but Linux will be in everything: your fridge, your TV, your car, your electrical system, your water and sewage systems, your phone, you’re neighbors who are flying robotic UAVs to peek in your windows. Everything.

My day job is building a radar system for UAVs (the big ones) that use embedded Linux to run out of flash. But the direction of interest is smaller devices, little boards with processors and memory in one, like the Pi or BeagleBoard, that can sense the environment and communicate to the rest of the household, with one of those devices used to display all the info on a big wall, removing the need for specialized devices just for the purpose of display.

Anyway, I’m really into making my own custom distribution based on Crosstool-NG (for cross compiling), u-boot (bootloader), Buildroot/Busybox (for root filesystems) and of course Linux.

Related posts:

See this post for links to other interviews here and a couple people who have interviewed me.

Fifteen interviews

Seven Nine people I have interviewed:

Two Four people who have interviewed me:

Six interviews I have blogged about:

Evaluating weather forecast accuracy: an interview with Eric Floehr

Eric Floehr is the owner of ForecastWatch, a company that evaluates the accuracy of weather forecasts. In this interview Eric explains what his business does, how he got started, and some of the technology he uses.

JC: Let’s talk about your business and how you got started.

EF: I’m a programmer by trade. I got a computer science degree from Ohio State University and took a number of programming jobs, eventually ending up in management.

I’ve also always been interested in weather. A couple years ago my Mom showed me my baby book. At five years old it said “He’s interested in space, dinosaurs, and the weather.” I’m not as interested in dinosaurs now, but still interested in space and the weather.

When I was working as a programmer, and especially when I was a manager, I liked to do little programming projects to learn things. So when I ran across Python I thought about what I could write. I’d wondered whether there was any difference in the accuracy of various weather services — AccuWeather, Weather.gov, etc. Did they use different models, or did they all get their data from the National Weather Service and just package it up differently? So I wrote a little Python web scraper to pull forecasts from various places and compare it with observations. I kept doing that and realized there really were differences between the forecasters.

I didn’t start out for this to be a business. It just started out to satisfy personal curiosity. It just kept growing every year. In my last position before going out on my own I was CTO for a company that made a backup appliance. We got to the point where the product was mature and doing well. ForecastWatch was taking more and more of my time because I was getting more business from it, and so I decided to make the switch. That was March 2010. Revenue doubled over the next year and and it looks like this year it will double again. Things are going well and I really enjoy it.

JC: So you hadn’t been doing this that long when we met last year at SciPy in Austin.

EF: No, I’d only been doing this full time for a few months. But I’d been doing this part-time since 2004.

I didn’t have full-time revenue when I was doing this part-time. But it’s amazing. Once you have the time to focus on something, the opportunities that you hadn’t had time to notice before suddenly open up. Just the act of making something your focus almost makes your goal come to fruition. For years you think “too risky, too risky” and then once you make that jump, things fall in place.

JC: So what exactly is the product you sell?

EF: There are two main components. There’s an online component that is subscription-based. It provides monthly aggregated statistics on forecasts versus actual observations. It has absolute errors, min and max errors, Brier score, all kinds of statistics. It evaluates forecasts for precipitation, high and low temperature, opacity, wind speed and direction, etc. Meteriologist use those statistics to evaluate their forecasts to see how they’re doing relative to their peers.

The second component is research reports. Sometimes meteorologists will commission a report to show how well they’re doing. These reports are based on standard, widely-accepted metrics and time-frames, so they can’t just cherry-pick criteria they happened to do well on. But if they see there are statistics in ForecastWatch where they are doing really well, they might want to tell their customers. I’ve also created reports for media companies, large Internet service providers, energy trading companies and other companies who were evaluating weather forecast providers or want some other data analysis related to weather forecasts.

Something else, and I don’t know whether this will become a major component, but another area some people are interested in is historical forecasts. I have agreements with some of the weather forecasting companies to sell their forecasts that are no longer forecasts. Some people find this information valuable. For example, a marketer with a major sports league wanted to know how weather forecasts affected attendance. Another example was an investment manager who was looking to invest in a business whose performance he believed had some correlation with weather forecasts. For example, a ski lodge might want to know how far out people base their decisions on forecasts.

I have this data back to 2004. It’s funny, but most weather forecasting companies historically have not kept their forecasts. Their bread-and-butter is the forecast in the future. Once that future becomes the past, they saw no value in that data until recently.

Incidentally, because I’m monitoring weather forecasters’ web sites, I sometimes let them know about errors they were unaware of.

JC: What volume of data are you dealing with?

EF: I have about 200,000,000 forecast data points back to 2004. I’m adding about 130,000 data points a day. My database is something on the order of 70 GB. That’s observation data, hourly forecasts, metadata, etc. Right now I’m looking at data from about 850 locations in the US and about 50 in Canada. I’m looking to expand that both domestically and internationally.

JC: So what kind of technology are you using?

EF: I’m running a LAMP stack: Linux, Apache, MySQL, Python. Originally I was on Red Hat Linux but I’ve switched to Ubuntu server. I’m using Django for the web site. Everything is in Python: the scrapers are in Python, the web site is in Python, all the administrative back-end is in Python.

There are two web sites right now: ForecastWatch.com, which is the subscription, professional site, and a free consumer site ForecastAdvisor.com. The consumer site will give you a local forecast and a measure of the accuracy for various forecasters for your weather.

JC: And who are your customers?

EF: All the major weather forecast companies. Also some financial companies, logistics and transportation companies, etc. I’m just starting to expand more into serving companies that depend on meterological forecasts whereas in the past I’ve focused directly on meterologists.

JC: Let’s talk a little more about the entrepreneurial aspect of your business.

EF: Well, for one thing, I don’t think I’d ever have done this if I’d thought about doing it to make money. There’s not an enormous market for this service, but in a way that’s good. I came from a completely technical background. There’s not a marketing or sales gene in my body and I’ve had to learn a lot. ForecastWatch has given me a great opportunity to learn about those non-technical areas of a business that were so foreign to me before.

I got into this entirely for my own use. And I thought that maybe there was already something that did what I wanted, and in the process of trying to find what’s out there I discovered an unmet need. Even though all the major forecasters said that accuracy was the number one thing they were interested in, they weren’t effectively measuring their accuracy. I thought that if I’m interested in this, maybe other people are too.

At first pricing was a mystery to me. Maybe I needed a new laptop, so I’d charge someone the price of a laptop for some analysis. I had to learn the value of my time and my product.

***

Some talks by Eric:

PyOhio 2009 talk about ForecastWatch
PyOhio 2010 panel on Python and entrepreneurship
SciPy 2010 talk

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More interviews
More on entrepreneurship
More on Python

Why Food for the Hungry runs Ubuntu

Rick Richter is CIO of Food for the Hungry. In this interview Rick explains why his organization is moving all of its computers to Ubuntu.

Ethiopian farmer Ato Admasu

Ethiopian farmer Ato Admasu. Photo credit Food for the Hungry.

John: Tell me a little about Food for the Hungry and what you do there.

Rick: Food for the Hungry is a Christian relief and development organization. We go in to relief situations — maybe there has been a natural disaster or war — and provide life-sustaining needs: food, shelter, whatever the need may be.  For example, the recent earthquake in Haiti. But the other part of what we do is the sustained, long-term development on the community level. The idea is to work with leaders and churches to better take care of themselves rather than relying on outside organizations for support.

I’m the CIO. I’m in charge of the information and technology for the organization. We’re in 25 countries. I have staff all over the world, about 25 people. There are about 12 who work directly for global IT, mostly in Phoenix, and the rest in various countries.  There are also people who work directly for local offices, for example in Kenya, that coordinate with global IT. We’re responsible for about 900 computers.

John: You and I were talking the other day about your organization’s project to move all its computers over to Ubuntu.

Rick: We started an informal process to convert to Ubuntu two and a half years ago. It started when my son went to Bangladesh. He spent the summer there and converted some of their computers to Ubuntu. At first we didn’t have full management support for the process. They don’t really understand it and it scares them.

There were individual country directors interested in the project and I talked it up. There’s some independence in the organization to make those kind of decisions. Now, for the first time, we have full support of management for the conversion on a wide scale. I’m going to Cambodia next week. Right now they’re all running Windows but before I leave they’ll be running Ubuntu. In Asia we probably have about 80% of our computers on Ubuntu. We don’t have big offices in Asia. Our bigger offices are in Africa and they’re a little slower to adopt. Until now, a lot of it depended on whether the local country director was ready to change.

We found it was important for a number of reasons. One is security. Linux is not as vulnerable to viruses. We have so many places where entire computer systems have been totally crippled because of viruses. A lot of networks are very primitive, so the network is basically a thumb drive between offices in a country. A thumb drive is the best way to transmit viruses you can find.

We’ve also found in the last few years anti-virus software has become less and less effective. Three or four years ago, if you had up-to-date anti-virus software you wouldn’t get a virus. These days, you still get them. Some of our staff have other jobs within FH besides their IT responsibilities and may not have a lot of IT experience. As a result, staff often do not have the time to pro-actively manage IT.

Another issue is maintainability. Windows computers don’t run as well over time. With Ubuntu, when we come back to a computer two years later it’s in as good a shape as we left it.

Linux requires much less hardware to run than Windows. We have eight- or nine-year-old computers at a lot of our sites that will no longer run or barely run Windows.

John: So saving money on software licenses is a benefit, but not the main consideration.

Rick: Saving money on licenses is important, but it’s not the driving force. We’re a non-profit and we have a contract with Microsoft where we get pretty good prices.

Another reason for moving to Ubuntu is that in some countries it is very difficult to legally obtain licenses. Sometimes it’s next to impossible. You can’t buy legal Microsoft licenses in some places, or if you can, the price is outrageous. So many legalities and so many weird hoops you have to jump through.

As a Christian organization we need to set a good example and make sure all our licenses are legal. We want to be clear and up-front about our software. Ubuntu eliminates that problem.

John: What experience have you had retraining your IT people to support Linux?

Rick: We have IT professionals and we have people who are much less skilled. Most of the IT people who do the support have really bought into it. They’re excited about it and they’re pushing it. Those who do support in the field who have had less exposure, some of them have bought into it, some have not as much. It requires time. It requires dedication. It also required commitment from their management.

Related posts:

Applied topology and Dante: an interview with Robert Ghrist

Robert Ghrist A few weeks ago I discovered Robert Ghrist via his web site. Robert is a professor of mathematics and electrical engineering. He describes his research as applied topology, something I’d never heard of. (Topology has countless applications to other areas of mathematics, but I’d not heard of much work directly applying topology to practical physical problems.) In addition to his work in applied topology, I was intrigued by Robert’s interest in old books.

The following is a lightly-edited transcript of a phone conversation Robert and I had September 9, 2010.

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JC: When I ran across your web site one thing that grabbed my attention was your research in applied topology. I’ve studied applied math and I’ve studied topology, but the two are very separate in my mind. I was intrigued to hear you combine them.

RG: Those two are separate in a lot of people’s minds, but not for long. It’s one of those things that the time has come and it’s clear that the tools that were developed for very abstract, esoteric problems have really concrete value with respect to modern challenges in data, or systems analysis.

JC: Could you give some examples of that?

RG: Certainly. One of the first groups of people who do full-scale applied algebraic topology were Gunnar Carlsson’s group at Stanford doing applications to data analysis. The setup is you have a collection of data points in a space, a point cloud, that is a discrete representation of some interesting structure. For example, you might want to know how many connected components does this data set have. That might correspond to different features. For example, this might come from customer surveys that a corporation has out. It’s trying to cluster these customers. Or if it is medical data, say they are trying to discern different types of cancers. Then you might look at what statisticians call clustering, grouping data sets into connected components.

Well, topologists know that’s just the first step in a larger program of finding global structure. Besides having connectivity properties, spaces can have holes in them of various types. There are formal algebraic methods for finding and classifying those holes. That’s homology, cohomology, homotopy theory. And applying that to data turns out to give some really revolutionary techniques that don’t rely on projecting the data set down to a two-dimensional picture and trying to visualize what’s happening. It’s automatic.

There are similarly themed application in the work I do in engineering systems where you take data that comes from, say, a network of sensors or a communications network or a networked connection on computers or a networked collection of autonomous robots. And you try and take all that local information, say in the context of sensor networks, you take collections of local data and try to patch it together to give you global understanding of an environment. That kind of local-to-global transition is what the techniques of topology were built to do. And they are surprisingly efficacious in these very applied problems.

JC: I’m familiar with Van Kampen’s theorem in homotopy. Is that the sort of thing you’re talking about?

RG: Yeah, homotopy tends to be less computable than homology. Homology is much more natural in these contexts. The corresponding principle is the Mayer-Vietoris principle, the homological analog of Van Kampen. And the Mayer-Vietoris principle is really telling you something about integration, how you stitch together local bits of data, how you integrate it into a global understanding of your network. That is a very deep idea that is very important to transitioning from local to global data.

JC: One mental block I have when I’m thinking about these sort of things is that in my mind topology seems sorta fragile in the sense that one random connection can change something. Connect just one pair of dots and suddenly a disconnected space becomes a connected space. It seems that would be a problem in these settings where you make some sort of topological statement, but any missing data or erroneous data invalidates your conclusions. But I remember you said something that was sort of the opposite on your web site, that topological methods can be more robust. I could see that, but I’m having trouble resolving these two views.

RG: There are different types of robustness that are critical in different types of applications. Because the constructs of algebraic topology are invariant under homotopy or deformation, it turns out to be very robust with respect to, for example, coordinate changes. That is extremely useful when you’re dealing with data that has some anchor to the physical world.

Let’s say data that’s being collected by our cell phones. Put a couple sensors on a cell phone and we have lots and lots of interesting data streams. And that data is tied to physical locations. But you might not know exactly where it is. GPS doesn’t work so well when you’re inside a building, for example. In contexts like that, you want the kind of robustness that doesn’t depend on having a carefully laid-out coordinate system.

Now robustness with respect to noise, especially robustness with respect to errors, is a much more difficult problem to solve in general. But even in that case there are some topological tools that in specific examples can be deployed. This gets into slightly more technical stuff involving persistent homology and topological properties that persist over a range of samplings.

JC: Could you give an example of how knowing the homology of a data set might tell you something about a physical phenomena?

RG: One example that I’ve worked with a lot has to do with coverage problems in sensor networks. Let’s say we’re talking about cell phone coverage, because everyone’s familiar with that. If you get into a hole in the cell phone network where you’ve dropped coverage, that’s frustrating. You’d like to know whether you have full coverage over an area or not, whether you have holes.

This gets much more critical when you’re talking about a security setting. You have video cameras or satellites that cover a region and you want whether you’ve covered everything, or whether there are holes where you are missing information. One of the things I’ve used homology theory for is to give criteria that guarantee coverage, that guarantee no holes in your sensor network based exclusive on coordinate-free data. So even though the sensors may not know where they are, and only know the identities of the sensors near by, it’s still possible to verify coverage based on homological criteria.

JC: Interesting. I suppose especially if you’re looking at higher-dimensional data you can’t just draw a lot of circles on a map and see whether they overlap. You have to do something more computational.

RG: Exactly. Especially if those circles are in motion and you want to know what’s happening over time. Especially if there are no coordinates and you don’t know where to draw the circles to see how things overlap.

One thing I want to get across when I’m talking with people is that I view a mathematics library the same way an archaeologist views a prime digging site. There are all these wonderful treasures that are buried there and hidden from the rest of the world. If you pick up a typical book on sheaf theory, for example, it’s unreadable. But it’s full of stuff that is very, very important to solving really difficult problems. And I have this vision of digging through the obscure text and finding these gems and exporting them over to the engineering college and other domains where these tools can find utility.

Now, a lot of esoteric mathematics has already crossed the fence. No one will claim any more that number theory is useless. But topology is the place where you have the most-useful, least-used tools. So that’s my vision for what I want to see happen in mathematics and what I’m trying to accomplish.

JC: Switching gears a little bit, another thing on your site that caught my eye was your quote about old books.

Reading anything less than 50 years old is like drinking new wine: permissible once or twice a year and usually followed by regret and a headache.

I thought about C. S. Lewis’ exhortation to mix in old books with your reading of new books because each age has its own blind spots. Old authors have their own blind spots, but maybe they’re complementary to the ones we have.

RG: Exactly. I definitely have followed that dictum. Maybe a little too much so, in that I rarely read anything modern at all. When it comes to books. I don’t follow that rule when it comes to music or movies or blogs. But on the level of books, there is so much good stuff out there that has stood the test of time, I don’t run out of interesting things to read. I had the wonderful experience as a college student to take a great books-type course that involved a lot of reading, a lot of discussion. Really changed my outlook and got me loving the classics and really living inside a lot of those books.

JC: Were you a math major when you took this great books class?

RG: No, I was an engineering major. My undergraduate degree was in engineering. I came to math a little late in life.

JC: You said you were particularly fond of Dante.

RG: That’s correct. Yeah, I’ve lived in that book [The Divine Comedy] a long time and I still find new and very engaging ideas in it every time I crack it open. Most people don’t get very far past the Inferno. The Inferno is the exciting, action-movie part of the story. But the later parts of the story — purgatory, paradise — those are really nice places to live.

JC: Have you had to do a lot of historical research to be able to read Dante?

RG: If you get a good translation with a good set of notes, that makes it much easier. I find the translation by Dorothy Sayers has excellent notes. She got turned on to Dante late in life. There’s an interesting story. While they were having bombings in the early 1940’s, she was going down to the bomb shelter to spend a few hours, she decided to grab a book off the shelf on the way down. She saw a copy of Dante. She said “You know, I’ve never really read Dante.” Pulled it off the shelf. For the next two days she didn’t eat or sleep. She was engrossed with the story and how masterful it was. And she wound up devoting the rest of her life to mastering the Italian and producing her own translation.

Other interviews:

A few questions with Frederick Brooks

The shelf life of software development books is typically two or three years, maybe five or ten years for a “classic.” Frederick Brooks, however, wrote a book on software development in 1975 that remains a best-seller: The Mythical Man-Month. His book has remained popular because he wrote about human nature as applied to software development, not the hottest APIs and development fads from the 1970’s.

Frederick Brooks has written a new book that should also enjoy exceptional shelf life, The Design of Design: Essays from a Computer Scientist. In this book, Brooks looks back over a long successful career in computing and makes insightful observations about design.

Frederick Brooks, Jr.

The following interview comes from an email exchange with Frederick Brooks.

JC: You did a PhD in math with Howard Aiken in 1956. Did you study numerical analysis? Did you intend at the time to have a career in computing?

FB: Oh, yes indeed. That’s why I went to Aiken’s lab for graduate work.

JC: I was struck by your comments on conceptual integrity, particularly this quote: “Most great works have been made by one mind. The exceptions have been made by two minds.” Could you say more about that?

FB: I give lots of examples in the book of the one mind case, and a few of the two-mind case.

JC: You said in your book that your best management decision was sending E. J. Codd to get his PhD. That certainly paid off well. Could you share similar examples of successful long-term investments?

FB: Well, IBM’s decision to gamble everything on the System/360, terminating six successful product lines to do so, is a great example. DARPA’s funding of the development of the ARPAnet, ancestor to the Internet, is another great example.

JC: What are some technologies from decades ago that are being rediscovered?

FB: I find it useful to write first drafts of serious things, such as scientific papers and books, by hand with a felt-tip pen. I can type faster than I can think, so composing on a keyboard yields unnecessary wordiness. Writing by hand matches my thinking and writing speeds, and the result is leaner and cleaner.

JC: What are some that have not become popular again but that you think should be reconsidered?

FB: Probably the previous example answers this question better than it does the previous question.

JC: Apart from technological changes, how have you seen the workplace change over your career?

FB: I’ve been in academia for the past 46 years. The biggest change in academia is a consequence of personal computers and networks: faculty members don’t use secretaries as such, they write their own letters, and make their own phone calls. Our assistants are indeed administrative assistants, rather than secretaries.

JC: What change would you like to see happen as a result of people reading your new book?

FB: Even more recognition of the role of a chief designer, separate from a project manager, in making a new artifact, and more attention to choosing and growing such.

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Update: Three years after this interview, I had a chance to meet Fred Brooks in person at the Heidelberg Laureate Forum.

Related links:

Other interviews: