Tag: english

A meditation on recreational essay-writing

Posted by – December 2, 2015

Writing is one of those things I really enjoy, but has become such a mentally and emotionally complicated activity that I find myself shying away from it, or stopping in the middle of without finishing. Note that the problem usually isn’t distractions or laziness, but my own mental dialogue getting in the way.

From the technical (Should I write a long comment on this guy’s blog or write a blog post? A forum post? A tweet? A Facebook update?) to the practical (Should I write in Finnish, since I am Finnish and often think about Finland-centric things? Perhaps I only think about Finnish stuff because I write in Finnish? That’s so insular.. But do I really think I have an audience anyway, so what does it matter what language I write in?) to the psychological/philosophical (Who do I think I am to write at all? Have I really examined my reasons for this mental exhibitionism? Should I write anonymously? But isn’t that kind of cowardly? Everything I write is shit, but then again it’s the only way to get better.. But better for what? Don’t I already hate most of what I read anyway? Why add to the trash-heap?), doubts and insecurities undermine the whole effort.

When I was in school, I used to enjoy writing in school publications. Unbelievably in retrospect, the first one we started out of our own initiative in elementary school (ages 6-11 for me) with my best friend at that time. Published fortnightly for about three years, except during holidays, it featured absurd humour, true and invented schoolyard happenings and music reviews. My friend’s mother photocopied them, we sold issues for two marks each and were read with interest which we stoked with manufactured scandals. It was a lot of fun, and our main hobby.

Then at the next stage of school (12-14) there was a real school paper run like a club by the Finnish teacher. Enthusiasm among the staff was much lower, as it always is with official things, and it wasn’t that much fun, but it was still one of the better things that happened in that school (which occupies a pretty horrible place in my memories). At that time I also blogged, before that was really a thing. Those writings have mercifully disappeared both from the Internet and my recollection.

Then in upper secondary school (15-18) there was quite a flourishing of publications while I was there: an official school paper for school credit which I wasn’t involved with; a leftist political paper, in one issue of which I wrote half the articles (the editor wrote the other half); an amazingly high-quality popular science publication where I wrote two articles that somehow still haunt me today, someone having run into them and telling me about it or asking about them; and a cultural review. This in a school of 600 pupils! I could say “those were the days”, but of course now I’d have difficulty reading through those things for embarrassment. Still, it was a great thing to do, even if we only did it in hopes of fame and recognition.

That’s what most writing of that sort is for anyway. I figure it like this: writing on social media is group signaling (this is who I am) and writing seriously in blogs or unpaid publications is personal signaling (look at me, I’m so smart). I tend to agree with Samuel Johnson (who I was partially named after), who said “No man but a blockhead ever wrote, except for money.” So I really should place all those columnists-for money who I despise above myself. That’s something I struggle with. But I digress..

After that I started another blog, on LiveJournal, and later another on hardwick.fi. There I wrote some hundreds of posts, but often personal, which doesn’t really count. It was at this time that matters of audience started bothering me. Sometimes I’d write about mathematics or chess, and know that very few people would be interested. The language question is another surprisingly intractable problem. Writing in Finnish vs. English feels different, it comes out different and in terms of audience they’re compatible in one way – Finnish people have no problem reading English at quite a high level – but in practice Finns are biased towards reading Finnish language stuff, so it’s attractive to make use of that connection.

Perhaps most serious of all is the problem of honesty and intellectual climate. When I was younger, I had no idea how stupid I sounded and didn’t care if people thought badly about me because of what I wrote. Now I am very aware of the sensitivity and strength of people’s judgments. Most people in my life I meet very seldom face-to-face, the only connection being indirect communication on the Internet (meaning, not even personal messages but public posts). I worry about alienating them the way I see people doing all the time on social media. As I write, there is even a signaling war over what type of Facebook profile picture one should have in the wake of the terrorism that occurred in Paris last Friday night. On Twitter I write in Finnish about my stupid and hateful political opinions and have turned off lots of people I know and like, and attracted people I don’t know and probably wouldn’t like.

I don’t think these limitations are necessarily a bad thing (we would all be monsters if it weren’t for concern over appearances), but I want to find a way to live with them and still express myself somehow and practice thinking & writing. There’s always anonymous writing, which I’ve done quite a bit of in the past few years, but unconnected to myself it just disappears into nothingness, which ultimately I guess I just don’t want to happen. These days I just read a hell of a lot on the Internet. I’ve already read over 5000 blog posts this year, and God knows how many comments. It’s a great world out there (really!) and I would like to be a part of it.

One has to compartmentalise. Right now I’d like to get back to writing in Finnish on my blog, rather than write these long Facebook posts in English when I’m not too tired (I don’t understand how anything gets done either in hot countries or by people with young children). Forgoing a potential English-language audience is too bad, but it’s a safe place to practice. If I ever write anything good I can always translate it.

From the Games People Play department

Posted by – December 2, 2015

A, 2-year-old male, lying on a changing table
Me, 30-year-old male, standing in front

[A kicks me in the stomach.]
Me: No kicking.
A: Kicking!
[A kicks.]
Me: No kicking.
A (laughing): Kicking!
[A kicks.]
Me (laughing): No kicking!
A (laughing maniacally): Kicking!
[A kicks.]
Me (serious): No kicking.
A (screaming with laughter): Kicking!
[scene continues like this forever]

Status redistribution

Posted by – December 2, 2015

It has become clear in modern welfare societies that redistribution of wealth is inadequate as a guarantor of social well-being. It is possible for people to get through years, decades or an entire lifetime without working a job, subsisting through various interactions with the public welfare system, but only a very individualistic and self-satisfied sort of person is able to achieve happiness in such a life. Indeed, judging from personal accounts, prolonged interaction with the system practically guarantees depression and feelings of worthlessness. Escapism into drunkedness or drugs often follows, and is considered a pity.

Sometimes, however, people escape into an intense appreciation of a hobby or subculture, and that is not considered such a pity. Indeed, this is a point often raised in the context of universal income (or negative income tax, or similar schemes), that when subsistence no longer requires conforming to the demands of the system (pretend to apply for undesirable jobs, ineffective training, be diagnosed as having a mental illness so you can be excused from obligations), people would be more free to pursue such self-actualising goals. “Free of what?” is an interesting question. Time constraints? Their own negative emotions like guilt? The mental distress of having to lie and self-justify? But I’m not going to address that now.

Ronald Dworkin published a pair of essays called “What is Equality?” in the 1981, the first addressing “equality of welfare” and the second “equality of resources”. (Years later he continued the series with “the place of liberty”.) They constitute a rather good exploration of what a complicated question equality really is. From the first one:

Suppose, for example, that a man of some wealth has several children, one of whom is blind, another a playboy with expensive tastes, a third a prospective politician with expensive ambitions, another a poet with humble needs, another a sculptor who works in expensive material, and so forth. How shall he draw his will? If he takes equality of welfare as his goal, then he will take these differences among his children into account, so that he will not leave them equal shares.

[…]

When the question arises how wealth should be distributed among children, for example, those who are seriously physically or mentally handicapped do seem to have, in all fairness, a claim to more than others. The ideal of equality of welfare may seem a plausible explanation of why this is so. Because they are handicapped, the blind need more resources to achieve equal welfare. But the same domestic example also provides at least an initially troublesome problem for that ideal. For most people would resist the conclusion that those who have expensive tastes are, for that reason, entitled to a larger share than others. Someone with champagne tastes (as we might describe his condition) also needs more resources to achieve welfare equal to those who prefer beer. But it does not seem fair that he should have more resources on that account. The case of the prospective politician, who needs a great deal of money to achieve his ambitions to do good, or the ambitious sculptor, who needs more expensive materials than the poet, perhaps falls in between. Their case for a larger share of their parent’s resources seems stronger than the case of the child with expensive tastes, but weaker than the case of the child who is blind.

Dworkin introduces several theories of equality, one of which is a family called “success theories of equality”:

These suppose that a person’s welfare is a matter of his success in fulfilling his preferences, goals, and ambitions, and so equality of success, as a conception of equality of welfare, recommends distribution and transfer of resources until no further transfer can decrease the extent to which people differ in such success.

[…after talking about more theories of equality, which] raise the question of whether equality in that conception is reached when people are in fact equal in welfare so conceived, or rather when they would be equal if they were fully informed of the relevant facts. Does someone attain a given level of success, for purposes of equality of success, when he believes that his preferences have been fulfilled to a given degree, or rather when he would believe that if he knew the facts?

That last part is very interesting to me. It cuts two ways: sometimes people rage against their lack of success, and I feel like telling them they expect too much, are unrealistic, that they really have had their preferences fulfilled rather well if only they could see it, all things considered (“look, you’re not smart or hard-working enough to be as good as the best, but you have no right to expect to be”). Other times people seem to achieve happiness through ignorance, misunderstanding either their relative success in their pursuit, or the relative importance of their pursuit.

But then it occurs to me that there is really not much difference between what I called ignorance about the relative importance of their pursuit and “escape” into hobbies or subcultures. Of course, there are very loaded words. In our postmodern world, there is no need to put down “marginal” pursuits; shared narratives about what is meaningful have broken down into ever smaller pieces, and there is no objective hierarchy of legitimacy among the narratives.

So ultimately, will our path towards equality take the form of producing a large enough number of subcultures, interests and hobbies that generate preference-satisfaction in the sense of the success theory of equality? It seems we have at least gone some way on that path, although I doubt it will amount to an actual paradise of social well-being (at least until people move on to living in simulated realities on computers). Subcultures, interests and hobbies we have always had with us, but only now in the kind of intense bubble way that truly create feelings of success.

As an aside, there have been islands of this type of thing before; Pythagoras’ pupils isolated themselves from outside value systems and made themselves the only possessors of truth and beauty, and many religious cults have followed the model, but that has only ever been possible for relatively small numbers of people. Mass religions have tried to produce feelings of success in other ways (“suffer in this earth, you will have a glorious reward in the next”), but they either never really worked or have stopped working in the present era.

The endgame of this development is hard to predict, but it seems to be rather unstable. Feelings of success create pride and an expectation of dignity and respect, but the atomization of society destroys solidarity on the national level (and solidarity on any other level doesn’t really exist). The harsh reality of producers vs. consumers will persist and become even sharper. Of course, much depends on the advance of technology. Many western countries already use some promilles of their GDP on foreign aid; perhaps one day that will be sufficient to support most of the population and their success-theory-of-equality bubbles.

That, of course, is on the big scale. It’s hard to see one’s own place in it clearly, but on the individual level, my advice is to neither try to escape nor to relentlessly play the status game, but to try to achieve some measure of inner peace, to have modest material needs and to develop sustainable and robust methods to satisfy them indefinitely. The only winning move is not to play?

Regarding counter-propaganda

Posted by – December 2, 2015

There is a category of books that I’ve really gotten something out of, but have a dubious reputation. They are books that make an explicit point, repeat the point, underline it, underline the underlining, make the same point again, add some exclamation marks, boldface the point, write it in red – you get the idea. The Point is some kind of extremist position, out of odds with generally accepted truths. These books have failed to convince the world, and not without reason: they try to prove too much, are easily critiqued and discredit themselves. I have sometimes been embarrassed to talk about them positively, lest I discredit myself too.

Some examples:

  • Anything written by Ayn Rand. The joke goes “There are two novels that can change a bookish fourteen-year old’s life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs.” People who aren’t fans of Rand, especially on the left, tend to not just dislike Rand, but consider being influenced by her an indication of being childish, non-serious, selfish to the point of autism & fanatical.
  • Thomas Szasz’s writings on psychology. The titles tell the story: “The Myth of Mental Illness”, “The Medicalization of Everyday Life”, “Cruel Compassion: Psychiatric Control of Society’s Unwanted”. Szasz was a trained psychiatrist himself, but turned on the profession, critiquing the use of psychiatry and state control of medical drugs as control mechanisms; the unexamined tendency to medicalise and smother with false compassion; and the concept of mental illness itself. These positions strike most people as incautious and cruel to the mentally ill (“If you say mental illness isn’t real, you’re denying the reality of people’s suffering.”)
  • Noam Chomsky’s writings on world politics. Chomsky is a respected intellectual, but his actual positions putting the US on par with the worst ever human rights and war crime offenders are not usually taken seriously. For an excellent examination, see Scott Alexander’s review

I think it’s a mistake to completely dismiss any of these, even though I’m not a “true believer” in any of them. My view of them is that they constitute effective and useful counter-propaganda against a much larger body of propaganda I hadn’t previously been properly aware of.

I acknowledge that Ayn Rand’s books are one-sided and uncomplicated fantasies without serious literary merit, but something like that is what is needed to get the message through to many people. Ayn Rand’s intended message is that the only ethical mode of life is complete selfishness, that human relationships must contain no obligations or duty, that co-operation in art is impossible etc., all of which is too much. But consider, firstly, the huge historical backdrop of praising selflessness; the purpose of life as fulfilling duty to God, country and family; and the recent rejection of the idea of artist as creator. Consider secondly the powerful leftist tendency in schools and universities, ie. in places where bookish people spend a lot of time. Ayn Rand may be absurd, but so are many simplistic Marxist and “anti-imperialist” ideas that go unridiculed and are quite popular in those places.

I was personally a leftist in my youth, and though that had already passed when I read Rand, it probably did contribute to salting the earth, so to speak, on an emotional level. It undid some of the brainwashing I had in favour of collectivism and showed me the falseness often implicit in compassion. So Rand is something I keep in mind and might suggest to someone who seems to me to need the same cure.

Thomas Szasz I was first introduced to by one of my favourite living economists, Bryan Caplan, who wrote a really great essay called The Economics of Szasz (you can read a pdf here). Reading Szasz was a really surprising experience to me, because it flipped my preconception of “if you declare mentally ill people to be ‘really, truly sick’, you’re being kind to them” 180 degrees. Whether personality disorders and substance addiction should really be treated as part of life rather than as part of medicine is not yet completely clear to me, but Szasz sure opened my eyes about these important aspects of the philosophy of mind and power structures & their mechanisms.

Chomsky has written many books, articles and essays on the topic of US foreign policy and the distorted view of it pushed by the media. In many cases he goes through absolute mountains of evidence, making beyond any reasonable doubt the case that the misdeeds of powerful nations on “our” side are again and again covered up and justified, and those of the losers are emphasised and demonised. On the other hand, he has made serious mistakes himself, like downplaying or outright denying the genocide in Cambodia for essentially political, leftist reasons (you really should read that Slate Star Codex link). Would any reasonable person take Chomsky’s body of work as a guide to geopolitics and the history of the 20th century? No. But the vast majority of people in the west believe comforting lies about the moral superiority of the US, Europe, Israel, Japan etc. on the geopolitical scene, and should be counter-indoctrinated by Chomsky.

In a world ruled by PR and propaganda (which are the same thing, propaganda being the historically earlier term for public relations), I cannot see this type of extremism in the pursuit of truth as a vice. Whenever I encounter something extreme or absurd, I try to entertain the possibility that I am being offered another opportunity to defeat my own unexamined absurdities.

Of course, not everyone needs counter-propaganda for every topic, being of a naturally sceptical or moderate persuasion; in fact, probably the most educated are in most need of this type of deprogramming, being the most brainwashed in the first place.

Symptoms of fatherhood

Posted by – December 2, 2015

(or, as a way of answering the difficult question “what is it like to be a parent”):

I was reading “Rabbit, Run” by John Updike. The main character, Rabbit, has abandoned his wife, Janice, and two-year-old son, Nelson. Now his wife has given birth to their second child, and Rabbit turns up at the hospital.

“Now I’ll have somebody to side with me against you and Nelson.”
“How is Nelson?”
“Oh. Every day, ‘Daddy home day?’ until I could belt him, the poor saint. Don’t make me talk about it, it’s too depressing.
“Oh, damn,” he says, and his own tears, that it seemed didn’t exist, sting the bridge of his nose. “I can’t believe it was me. I don’t know why I left.”

Later, when Rabbit has come home and is talking to Nelson:

“Yop. Where Mommy?”
“At the hospital.”
“At hop-pital? Come back Fi-day?”
“That’s right. She’ll come back Friday. Won’t she be happy to see how clean we make everything?”
“Yop. Daddy at hop-pital?”
“No. Daddy wasn’t at the hospital. Daddy was away.”
“Daddy away”—the boy’s eyes widen and his mouth drops open as he stares into the familiar concept of “away”; his voice deepens with the seriousness of it—”very, very long.” His arms go out to measure the length, so far his fingers bend backward. It is as long as he can measure.

Before, I don’t think that would have moved me much, but knowing that that’s about how a little kid really thinks and speaks, it’s very poignant.

Chess doodle

Posted by – December 2, 2015

Managed to amuse myself by finishing a blitz game with a knight journey ending in mate.

Regarding answers and storytelling

Posted by – December 2, 2015

Yesterday at a (child’s) birthday party someone asked person A about how he came to know person B. He told us he’d taken a trip to Paris, and on the aeroplane he happened to strike up a conversation with someone else, C. They became friends that way, and then much later when he was meeting person C at a pub, person B, who was also friends with person C, was there, and that’s how they met.

Now, that’s a perfectly reasonable answer, but I remarked that he could just have said “Oh, we met via a mutual friend, C.” This prompted a rather lengthy and probably pointless discussion about the right way to give answers, and whether there’s an essential difference between answering questions and telling stories.

I have rather strong instincts about this sort of thing, and with regards to reciprocal communication, ie. not storytelling, was convinced by what I was taught in a linguistics course on pragmatics, namely that successful communication is characterised by adherence to certain cooperative maxims. These are often called Gricean maxims, after Paul Grice, and are in simplified form:

1. Say things you believe to be true and have evidence for
2. Give enough information, but not more than that
3. Be relevant
4. Be clear and easy to understand, avoiding unclear expressions, ambiguity, out-of-order chronology etc.

So I was exercised by the irrelevant addition of the trip to Paris and how A and C met. Of course, it’s not easy to say exactly where the line is. Even C’s identity is not really relevant, but had it been omitted (“We met via a mutual friend”), it would probably seem to be too little information, prompting “Oh, which friend?”

A argued that including the information about the plane trip was natural, because it closes the circle: there was no further person who introduced A and C, and therefore curiosity is satisfied. Also, from a storytelling point of view, it is somewhat unusual to meet someone spontaneously like that, so why not add it.

Of course, usually there *is* a further person D who made the connection, and it would be unreasonable to include information about that, and about how A and D and C and D met etc.

Now, what is the storytelling point of view? Arguably, since we were in a social setting, the storytelling frame is always available, since we’re really mostly trying to entertain each other rather than transmit information efficiently. In a workplace situation, you’re not supposed to start telling stories, because that’s wasting time. Perhaps the storytelling maxims are:

1. Say things you believe to be true and have evidence for, except if it’s more entertaining otherwise
2. Give enough information, but not more than that, except if it’s more entertaining otherwise
3. Be relevant, except if it’s more entertaining otherwise
4. Be clear and easy to understand, avoiding unclear expressions, ambiguity, out-of-order chronology etc. except if it’s more entertaining otherwise

I think for some people (perhaps those people who are known as “storytellers”), that’s really how it is.

In a conversation, it’s implied that communication should be most relevant to the most recent thing the other person has said. It’s a kind of back-and-forth of adjusting the topic from one message to the next. This is supported by the way a person will sometimes explicitly break this principle: “I’ll get back to that, but just let me tell you about…” In storytelling, the storyteller decides to take up the right to determine relevance himself. In his mind there is some central idea behind the story, not immediately known to everyone else, so he can break the rules, but hopefully come around to completing the story into an internally relevant whole.

When storytelling happens in the middle of conversation, people are very aware of it. “Ah, he’s stopped the conversation to tell a story.” This is considered to be quite a responsibility. If the storyteller fails to tie up the story in some interesting way or to be entertaining, he will very quickly come to be seen as a bore, in a much worse way than just generally failing to be interesting in his replies to question in the normal course of conversation.

Why do people you agree with seem more sophisticated?

Posted by – July 20, 2012

It’s a persistent trend that people on both sides of an issue tell themselves that their side is generally more nuanced and sophisticated than the other. Christians think that atheists are basically angsty teenagers with no sense of history or personal experience. Rightists think that leftists are over-emotional simpletons.

When these groups discuss matters amongst themselves, they don’t need to talk about the fundamental matters they agree on. Instead, they can move on to something deeper, and reveal what they themselves doubt or disagree on about the shared position. Leftists consider themselves to be deep thinkers, and they like to talk a lot about advancing leftism with other leftists, or about the best version of leftism. So leftism seems like a very large topic to them, whereas rightists practically ignore it.

When these opposing groups talk to each other, they’re constantly getting bogged down by the fundamental differences. The other side can’t even get the basics right! So of course they start thinking that the other side is simplistic, radical and can’t listen to reason. If only our side had their fanatical unity, maybe we could get somewhere…

Academics have to practice a lot to leave behind even a small part of this type of bias, but they do have some success. Consequently, they see non-academics on both sides as simplistic and non-nuanced. They are on a meta-level of sophistication.

Halla-aho convicted for hate speech

Posted by – June 8, 2012

Somewhat surprisingly, Finnish parliamentarian Jussi Halla-aho’s case, which progressed to the Finnish supreme court, has turned out even worse than it did in the lower courts. Previously he was convicted only for “disturbing the peace of religion” (“uskonrauhan rikkominen”, essentially a blasphemy law), but now the supreme court has also found him guilty for incitement to hatred against an ethnic or racial group (essentially hate speech).

Finland doesn’t have the best record in the world for civil liberties anyway, but this is nevertheless a considerable setback. For Finnish readers I’ve mirrored the original blog post here (the author has already been forced to redact parts, and this new decision demands him to make further cuts). A slightly subpar English translation may be found here.

I want to point out once again that one of the laws he was convicted under, the religious peace one, contains the phrase “who mocks God”. Finland is an EU country with an actively used blasphemy law.

Some words on the occasion of Vadim’s PhD defence

Posted by – November 21, 2011

My friend Vadim Kulikov defended his PhD thesis in mathematics this Saturday past. I hadn’t written anything down, but had had some thoughts circling around my head as to what remark I could make at the post-party (this is quite a big deal in Finnish academia). I did speak, and although it went on for longer than is ideal (even though I didn’t say everything I might have), it was so well-received I decided to give as good an account of it here as my recollection permits. I have made some improvements and additions, but I might also have forgotten something, so remind me if you were there and noticed an omission.

I was inspired to say something by the last heading in the Introduction in Vadim’s thesis, which all math students here should definitely read. It’s very motivational, describing the sense of fulfillment at not only having achieved something worth achieving, but also at having gained a truly deep understanding of something, in this case certain mathematical objects and ideas.

I got to thinking about what it is that has made Vadim progress faster and achieve more than most of his peers. Some things are obvious and indispensable: natural talent, a strong ability to work and concentrate, a deep love of mathematics and understanding, and some luck in having a suitable advisor. I believe these are sufficient to make a great student of mathematics, but something more is required to make a mathematician.

There is a concept in Zen buddhism, shoshin, meaning “beginner’s mind”. The saying is that “the beginner sees many things, the expert sees few things”. The beginner’s mind is empty and without preconceptions, so when the beginner encounters a thing, his mind is not filled with the few things he has been taught to think about it, but the totality of it.

For example, when appreciating a painting, the beginner sees a mass of brush strokes, a form, he might understand what the picture depicts – all in all, he is unguided and confused. As he gains knowledge, he starts to become an expert. He might identify the style of the painting and even the painter’s identity. He understands the use of various elements in the painting to signify ideas. He might know about the historical period in which the painting was created, and place the elements in that context. In brief, he gains the ability to see a painting, not be confused, have 5-10 thoughts about it and move on to the next one.

But at the highest levels of understanding, mastery, the Zen way is to have the beginner’s mind. The Zen master sees the mass of brush strokes. His mind is primed with every level of expertise, but it doesn’t force fixed ideas about what the painting is. It is full, yet empty.

There is actually some recognition of this in mathematics education at the university level. In many cases there is a simple way to solve an exercise if the student is aware of some higher-level theorem, without doing all the “boring” technical work you must do if you don’t know about the theorem. If a student presents such a solution, the lecturer will usually say “It’s nice that you know about this, but it would be better for you to do the problem without using this theorem, because it’s important to get to understand the internal details of these things.”

Vadim has a measure of this characteristic naturally, and I believe it is very valuable in doing creative work. One example of this is from when Vadim really had the beginner’s mind because he actually was a beginner. Vadim had come to our lukio (which the English might call a “sixth form college” and Americans might call “high school”) as a first year student, and I was a second year student. Vadim had already gotten enthusiastic about mathematics, but at his previous school there hadn’t been many other pupils with that interest, so he was happy to find a number of such people at our school. He was very eager to find problems to solve, so I told him to try to prove something during his next class; that every even number greater than two can be expressed as the sum of two prime numbers.

Well, as the mathematicians here have noticed, this is a famous open problem called Goldbach’s conjecture, so giving it to Vadim to solve was really just a practical joke on my part. “Someone’s too enthusiastic, let’s try to blunt his enthusiasm a bit.” Anyway, after the next class I asked Vadim how he’d gotten on and he said “I think I’ve almost solved it – I got the other direction, that when you add two primes you always get an even number.” I asked him, “What about 2 + 3?” “Oh, I forgot about that!”

When I revealed that the task was hopeless from the start, Vadim was not actually angry at me, or even all that deflated. To a beginner, all problems are open problems. Vadim even continued to think about the problem for some time, attacking it with whatever methods he knew about at that point.

So with the beginner’s mind there comes a certain fearlessness about open problems and unknown things. Vadim kept this more or less intact during his studies. In mathematics it’s important to have the “complete simultaneous understanding” of the (Zen) master and the open, fearless mind of the beginner, because you have to be able to transplant ideas from one part of mathematics to another part, understanding the internal details well enough to know what needs to be changed and what doesn’t. If you “see many things” like a beginner, you can have surprising ideas.

However, once he had begun work as a graduate student with Tapani [Hyttinen] and Sy Friedman, Vadim began to tell me about certain frustrations he was experiencing. Working with experienced mathematicians in their domain of expertise, it would always be they who had significant flashes of insight. Vadim could redeem himself by working out technical details, but time and again it felt like open problems could only be solved by these “oracles”. Instead of many things he was beginning to see only one thing, “this is an open problem so I can’t solve it”. In this way, the joy of mathematics and the creative spirit of the beginner’s mind was beginning to suffer.

So it was a great relief to Vadim (and a great pleasure for me to hear) when he had a major breakthrough completely on his own, and produced an idea that resolved an open problem. The angst of the open problem was swept away, and he could once again look at things with fresh eyes. So I’m happy he has passed through expertise to mastery of this field, retained shoshin, and hope that he’s able to keep it in other parts of life as well, leading to a fruitful life of many creative discoveries.