Tag: personal

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]

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.

The musée lapidaire in Avignon

Posted by – September 9, 2011

It never really occurred to me before that the impression of art history one gets from books and tv documentaries is extremely distorted towards high quality. The popular books want to get people excited about classical sculpture (say), so they show the very best of the best, from the geographic heartland and historical apex of classical sculpture. But of course most art is not as good as the very best, and in fact the median is usually rather crappy.

I had the opportunity to gain some insight into this yesterday when visiting Avignon, which has a sculptural museum with a permanent exhibit of mostly the Franco-Roman oeuvre from the early imperial period. Gaul was a comparative periphery, and its artists were mostly second-rate men who did a lot of headstones and workaday standard reproductions of the typical way the Roman/Hellenic gods were depicted.

This (I think) was a quite early Greek Athene:

This was some obscure fellow, by a French-Roman artist many centuries later:

A French-Roman scene from a Dionysian festivity:

The dancer on the right looks rather like Robert Crumb might have drawn her.

Also, a major invention of western civilization must have been inserting spaces between words, because these are super annoying to read:

Not everyone was bothered to make nice type:

SFCM 2011

Posted by – August 28, 2011

I’m back from my first ever scientific conference, SFCM 2011 in Zurich. My top two favourite talks were Lauri Karttunen’s keynote, Beyond Morphology – Pattern Matching with FST and Non-canonical inflection by Benoît Sagot and Géraldine Walther. An honourable mention goes to Morphology to the Rescue Redux: Resolving Borrowings and Code-mixing in Machine Translation by Esmé Manandise and Claudia Gdaniec. I demoed stuff for our HFST3 paper.

Karttunen presented some obvious-in-retrospect extensions to FST matching, rewriting and tagging and an implementation thereof in an algorithm/utility called pmatch. It’s mostly a combination of recursive transition networks and the insight that with some algorithmic trickery, it’s sufficient to match the end of a subpattern when you want to do left-to-right longest-match matching/tagging. The extensions he described most were

  • EndTag(), which is a command that gets compiled into special instructions for pmatch to wrap a pattern or subpattern in tags without the need to produce a transducer that’s always trying to output the start tag and enter failing transitions of the subpattern network, and
  • Ins(), which in RTN-style refers to a separate network to be pseudo-inserted at the current location.

These are achieved with flag diacritic -style special symbols, although pmatch itself doesn’t support flag diacritics. Hopefully we’ll have all this functionality in HFST one day, alongside flag-induced hyperminimization – an interesting topic I should write about one day. Put together, these techniques should significantly remedy the problems of networks becoming combinatorically huge in certain situations.


For the benefit of people who aren’t interested in computational morphology, here’s some travel stuff.

I’m not a big fan of travel, and was reminded why by almost everything going wrong. My flight was cancelled, and I had to queue for ages to be rerouted via Brussels, and almost missed that flight as well. All told, it took me over 10 hours to get from my house to the hotel in Zurich, leaving less time than I’d hoped to prepare for the demonstration session. And everything was sucky and expensive and my feet hurt and it’s just not worth it to ever leave home :(

Also, Blue1 is a terrible airline company and Swiss is nice (you get free chocolate).

Switzerland is about as orderly, clean and organized as you might imagine. A while ago a Japanese post-doc at the math department was leaving Helsinki to go to do math at an American university, and he sent a nice going-away email to people he’d met in Finland. He wrote “Finland is the 2nd most well-organized country among the places I have ever been (unfortunately you could not beat Japan, sorry!)” – I think he must have missed out on Switzerland.

Famous Swiss hospitality

(That said, there were definitely more representatives of ethnic minorities than in, say, Helsinki.)

The Swiss don’t mess around; each and every lamppost had a sticker like this:

Does it work?

I never saw a single extraneous piece of paper on these things.

Also, a little-known fact: Swiss people are in fact made out of polished steel.

I like the place. These guys know how to live.

End of intermission

Benoît and Géraldine had done work on a system for compactly describing certain irregular (“non-canonical”) phenomena in inflection:

  • suppletion (where some forms have an alternate stem or affixes)
  • heteroclesis (where some words have a mixed paradigm from several regular forms)
  • defectiveness (where certain forms are missing from the paradigm)
  • overabundance (where some forms have more than one realisation)
  • depondency (where certain words inherit part of another’s paradigm in the “wrong” context, eg. singular suffixation for expressing plural in some Croatian nouns)

They had used their approach to describe French irregular verbs, and also implemented several other well-known descriptions by French linguists. They wanted to show that their approach was best or most natural (at least most compact), and did so by estimating the Kolmogorov complexity of these schemes. This is something I’ve often thought about doing (examining linguistic theories by implementing them), so I’m happy that work is happening in this area.

Overall, SFCM was damn well organized, interesting, motivating and fun to attend – many thanks to the organizers, speakers and attendees!

Here’s to new experiences

Posted by – May 14, 2011

Went to see The Tiger Lillies, of which it perhaps suffices to say

(if you’re reading on Google reader, the object that’s supposed to be here doesn’t appear for some reason)

I’m crucifying Jesus, banging in the nails
and I am so happy, because old Jesus failed
I’m crucifying Jesus, nail him to the cross
The poor old bastard bleeds to death
and I don’t give a toss.

I’m bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails
I’m bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails
I’m bang – bang – bang – bang – banging in the nails
I’m bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails

I’m crucifying Jesus, in my piss he’s bathed
I think I am a pervert, I think I am depraved
I’m crucifying Jesus, beat him to a pulp
I stick my organ in his mouth and on it he must gulp.

I’m bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails
Bang – bang – bang – bang – banging in the nails
I’m bang – bang – bang – bang – banging in the nails
I’m bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails

You see that crown of thorns upon his head?
Well that was my idea!
I think I might be going to Hell
Oh… dear!
Bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails
Bang – bang – bang – bang – banging in the nails
Bang – bang – bang – bang – banging in the nails
I’m bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails!

Bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails
I’m bang – bang – bang – bang – banging in the nails
I’m bang – bang – bang – bang – banging in the nails
I’m bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails!

Bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails
I’m bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails
I’m bang – bang – bang – bang – banging in the nails
I’m bang, bang, bang, bang, bang, bang, bang, bang – banging in the nails!

Consider the chorus structure! I determined during the first half that this was music (and other performance) that warranted emotional participation rather than abstracted appreciation, so we rushed to take some universal fun enhancer during the interval, and it was exactly the right decision. We even got to briefly meet the guys after the show as they hawked records and autographs. Hard working band! Adrian Huge, the drummer, recommended The Brothel to the Cemetery, citing the above-given track.

It’s a strange thing to meet artists right after they’ve given a draining performance – they kind of wanted to connect with fans or whatever, but exuded a tired/wary sense of “these kids better not try to follow us to the pub”, which is of course completely understandable.

Not stopping there, day after next I got to meet Patri Friedman and other Less Wrong people at a meetup. We discussed meta-optimisation (how much should you concentrate on improving your processes, on improving the way you improve, on improving that etc. versus “just doing things”), dangerous opinions and liberal-mindedness, focus-enhancing drugs and of course seasteading. Hard working guy!

Cat urine backpack & relative differences of functions

Posted by – March 25, 2011

My backpack got stolen. It had just been urinated on by a cat, and was evidently beyond salvation (it was pretty beat up anyway). I emptied it and left it to stink outside of the pizzeria we’d decided to eat at, planning to take it to the next garbage bin I saw. But somebody nabbed it! I hope they don’t make the mistake I did of wearing the backpack – my nice winter coat now has a faint whiff of un-neutered male cat piss.

We were discussing Ramsey’s function (R(k) = the smallest number of people for which you can guarantee that either k people among them all know each other or k people all are strangers to each other) with Vadim. Its values are known to lie between {\sqrt 2}^k and 4^k, which is obviously quite a large gap. But how large? Vadim immediately said the difference 4^k- {\sqrt 2}^k is exponential, but it wasn’t so obvious to me. Eventually he convinced me. It then occurred to us that it’s in fact essentially 4^k; given a > b > 1, the difference between the gap and the larger exponential function relative to the larger function goes to zero, \lim_{x \to \infty} \frac{x^a - (x^a - x^b)}{x^a} = \lim_{x \to \infty} \frac{x^b}{x^a} = 0. So when you subtract a smaller exponential function from a larger exponential function, you’ve basically subtracted nothing. Which is really a stupid thing to notice because it’s true even of polynomial functions (but not linear functions).


Posted by – March 3, 2011

(Seen at the film archive’s theatre, Orion.)

Also, #aspekti, the irc channel for linguistic folks at the U of H, set out to collectively write a pornographic short story (in Finnish) with one word per contribution:

Olin diskossa. Sinä katsahdit jotakuta merkitsevästi. Otin taikurinhattuni repustani ja puin sen kaverilleni. Kaverini näytti minulle kännykästä välilihakuvia. Aloin kiihottua.

Lähdin kohti sinua päättäväisin vaikkakin väräjävin askelin. Sinä näit etäältä ilmeessäni jotain, joka sai olemuksesi hiuksenhienosti pelästyneeksi. Saavutin sopivan nopeuden karkottaakseni tarpeettomat hännystelijäsi. Nyt oli aika kuunnella kupeitteni kutsua.

Nostin sinut ilmaan kuin käärepaperin. Sinä söit aina niitä helvetin valkosipulikaramelleja. Kannoin sinut autolleni. Vaihdekeppi tarttui paidanliepeeseesi ja paljasti maidonvalkean kylkesi. Kaluni päätti laueta kalsareihin, mistä sait aiheen ruveta hihittämään ilkikurisesti. Päätin rangaista tästä jompaakumpaa, kaluani tai pilluasi. Päädyin valitsemaan molemmat.

Tartuin toimeen ja sitten hameeseesi. Vedin kaikki vaatteesi kumimatolle. Silmistäsi paistoi pelonsekainen himo. Kaluni ei ollut koskaan ollut toipunut niin nopeasti. Tiesit että olin valmis vaikka uskoin ettet koskaan antaisi anteeksi jos pakottaisin sinut ajattelemaan minua. “Sinä säälittävä mato”.

En murtunut tästä vaan kovetuin entisestään. Painoin taikanappiasi hellästi tupakansytyttimellä kunnes tajusin että se oli pois yhteisestä ajastamme. Vaihdoin otetta ja kuiskasin korvaasi “Et viitsisi antaa minun selviytyä tästä tästä voittajana?” Samalla olin ottanut kulauksen rohkaisevaa ja kaatanut sinut lasiini. Rintasi pullottivat revenneen toppisi lähellä. Asetuin niiden yläpuolelle kuin muinainen munainen Kolossus. “Palvo näitä kuin olisit saanut kohtauksen”, huusin lihasteni sykkiessä rytmikkäästi. Halusin koskettaa huuliasi mutta ne pelottivat paksuudellaan. Mistä olitkaan puhumassa? Kenties

It’s the kind of text that doesn’t really lose much on google translation (I cheated a bit by adding some words it missed):

I was a disco. I looked for someone you significantly. I took wizard hat from my backpack and gave it some characteristics friend. My friend showed me the meat of the mid-term mobile phone images. I started to become aroused.

I went towards you and decisive, albeit trembling steps. You saw from afar in my expression something that got your being frightened by a whisker. I reached a suitable speed to expel unwanted minions. Now it was time to listen to my loins invite.

Lift you into the air as the wrapping paper. You had always those damn garlic sweets. I carried you to the car. Grabbed the gear shift, and revealed your shirt hem milk white side. Decided to go off my dick underwear, where did you begin to rise giggle teasingly. I decided to punish this one, or my dick pussy. I decided to choose both.

I picked up the action and then your skirt. I pulled all the clothes in the rubber mat. Shining in your eyes the fear messy lust. My dick had never been recovered so quickly. You knew that I was ready even though I believed you’d never forgive if forcing you to think of me. “You pathetic worm.”

I do not fractured, but it harden even more. Your magic button gently pressed cigar-lighter until I realized that it was out of a common age. I changed the grip on your ear and whispered “You do not care to let me come out of this a winner here?” At the same time I took a sip of encouraging and knocked down you into my glass. Bulging breasts ruptured your top close. I settled above them as an ancient egg of Colossus. “Worship as you would have received such a scene,” yelled the muscles pulsing rhythmically. I wanted to touch your lips but they are scared thickness. Where were you all talking about? Perhaps

People like us #2

Posted by – January 29, 2011

I’ve been way too sick (terrible, horrible influenza, don’t recommend it for anyone) for a week for scanning, drawing or blogging, but I’ll just leave a brief prediction note here about the Egyptian protests before it’s too late. As I’ve previously noted, it’s suspiciously easy for people to choose sides in remote instances of unrest. Now everyone is on the side of the young, rights-demanding Egyptians who threaten to overthrow their government. My heart is, too, on their side, and I wish them the best of luck. However, my prediction is this: if they do succeed and Egypt undergoes a “regime change”, sooner or later the protesters will turn out to have been useful idiots for the islamists lying in wait. Sad face.

Art shock

Posted by – December 31, 2010

Inspired by tjic, a somewhat strange bedfellow, I’ve uncharacteristically decided to set myself a goal/resolution for 2011. I’ve set my sights a good deal lower than that fellow’s overcome-everything mindset (make money, build things, lose weight, learn instrument), but I’ll nevertheless be happy if I succeed. Heck, knowing me, I’ll most likely be happy even if I don’t! The goal is to make and publicly display 6 pictures a week for all of 2011. “Display” means “post here”, obviously. Turn off your RSS readers, gentlemen! I will probably do a post a week with the whole bunch. I hope to draw considerably more than 6 a week, but that’s what I aim to dare show and be bothered to scan and upload.

6 is probably more than I’ve done in a whole year most years. At the age of around 14-15 I had a period of sketching a fair bit, and again around 16-17 (I’m 25 now), so I’m very unpracticed and shoddy. In the latter part of 2010 I did some quick watercolours. But I do like drawing, a lot, and I hope this will improve my skill and make it even more fun. Perhaps more importantly, it would also be nice to get a habit of openness and willingness to reveal weaknesses in order to improve them.

My greatest weaknesses in drawing currently are probably in shading, perspective (I can’t think spatially for shit) and patience. I’ll probably start out by not attempting those, and attack them with more practice later.

Before I move on to show-and-tell, an anecdote about spatial thinking. This Thursday I was thinking about this Project Euler problem (by the way, skip this paragraph if you don’t want to be spoiled vis-a-vis the problem). I wanted to figure out a way to determine the shortest path from one corner of a cuboid to the direct opposite, using only the sides (if you prefer: in a room whose ceiling, floor and walls are rectangles, the shortest path for an ant to crawl from a corner on the floor to the opposite corner on the ceiling). My first idea was to find a suitable variable and differentiate: have the ant travel along the floor to some point x on the edge between the floor and an opposite wall, and then along the wall directly to the corner. x now determines the length of the path, so differentiate and find the zero of that function, and there you have it. Of course there are other ways to choose the path as well, so for each you have to derive the appropriate functions and do the same thing, and find the minimum from all those possibilities. The manipulations become rather hairy and fiddly… In a bar that evening I mentioned this to someone who almost immediately suggested that I could just fold the cuboid open and draw the paths as direct lines. Like this:

The blue cross is the starting point, the red crosses are points that map to the target corner, the three green paths are the possible minimal ones (except that with this diagram you can immediately see that it's never best to go across to a corner and straight up because it isn't a straight line).

The blue cross is the starting point, the red crosses are points that map to the target corner, the three green paths are the possible minimal ones (except that with this diagram you can immediately see that it's never best to go across to a corner and straight up because it isn't a straight line).

It’s all right triangles, easy peasy. This was so simple it took me a while to accept that this was really correct! This is what I mean by terrible spatial thinking ability.

Anyway. To give you some idea of where I am, here’s a bunch of recent sketches.

An impression of a table with a seated figure. The blue overhanging thing is a lamp.

An impression of a table with a seated figure. The blue overhanging thing is a lamp.

A quick bar sketch

A quick bar sketch

Another quick bar sketch. The mess on the forehead is a failed attempt at an eye. On the chin is not a beard, but another false start.

Another quick bar sketch. The mess on the forehead is a failed attempt at an eye. On the chin is not a beard, but another false start.

What prolonged drinking will do:

An impression of six people at a table (from my perspective, I was sitting at the head of the table - squint hard, youll see it eventually)

An impression of six people at a table (from my perspective, I was sitting at the head of the table - squint hard, you'll see it eventually)

My first attempt at a transvestite - not sure what I was thinking here

My first attempt at a transvestite - not sure what I was thinking here

For Finnish readers, a bonus: a selection of rather puzzling children’s stories with illustrations I wrote when I was 14 or so.