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Skiing and philosophy

Last autumn one of my closest friends started studying Philosophy at the University of Tampere. It is about twenty years since I graduated from the same department, so it has been interesting and inspiring to hear how the studies are nowadays. Sounds like not that much has changed - every year it is about a dozen of new people who start their studies, which means that the group of Philosophy students isn't that big, people quickly get to know each other. Also, the department personnel encourages students to be active - not just attending the lectures, but also to find their own field of interest. For example, a group of students can pick a book they are interested in, and organize a informal seminar where they read the book chapter by chapter and discuss it together. Then, if a student writes a paper about the book, the personnel will read the paper and that is considered a valid way of studying, equal to attending lectures and exams. Some of the best things in my own time of studying were such informal discussions with my fellow students. And now, when one of my friends is studying there, I have suddenly gained a fresh contact with the student life, with that sense of curiosity and inspiration, the joy of deep focused intellectual discussion.

I was told that this year, from January to May there will be a seminar where people don't read a book, but philosophical articles. A different article each week, presented by one of the students, and then discussion after it. Such an inspiring idea, for that will bundle together a wide variety of topics, different kinds of articles from different fields of philosophy. That was one of the other things I loved in studying - when the fellow students were interested in or specialised in topics which I wasn't that familiar with, a good discussion was a nice way to broaden perspectives, to get to hear about new topics. No need to read a heap of books all alone, when you can just listen to and ask questions from a person who has already read those books and has formed both an overall grasp of the general ideas, and often also some deeper insight into the details. So, just for the fun of it I decided to participate in that seminar. In these covid-ridden times everything is arranged so that it is not necessary to be physically present, a video call works as well. (My own presentation was already two weeks ago. I'll write about that in a later blog post, for I have a feeling that I'll need at least two posts for that, and that will take some time to write.)

Last week the article was "Conceptual and Computational Mathematics" by Nicolas Fillion (Department of Philosophy, Simon Fraser University, Canada). I've kept in mind that for me academical philosophy is now just an hobby, and my main project is coding Ancient Savo, and then doing a little of the necessary odd jobs to sustain myself. So I didn't find enough time to read all of the article (It is only 18 pages, well written, clear and easy to read). But what I managed to read was interesting and sparked some further thoughts and questions in my mind. I was looking forward to attend to the seminar, to hear the presentation by the person who had chosen this particular paper. That was Tuesday, a week ago. Before that the Monday was a full day of work for me. And Tuesday bit after noon I felt a need for fresh air - there was even some sunlight which is always precious in the wintertime when the days aren't that long. I decided to go skiing, for the first time this winter. It was about three hours till the seminar, so I'd have enough time for a nice cross-country skiing and then a meal before the seminar starts.

I skied down my driveway, planning to cross the fields to get to the lake ice. As I was on my way I met one of my neighbours, the elder fisher lady. We discussed animal tracks, and the local events (the typical countryside stuff - "is this or that neighbour still hospitalized, are they doing better now? You heard that house was sold to new owners?" etc.) The fisher lady invited me to come over to her place to have some coffee. I thought I'll have enough time for that, and some spontaneous social interaction is also nice. So we had coffee, and went into more details in our discussions. When I was about to leave she gave me a piece of cold-smoked pike, prepared by another neighbour. That was nice. So on I went, skiing to the lake, with a piece of cold-smoked pike in my pocket. This winter we have a proper layer of snow, but I'm not so sure if the lake ice is all safe. Also, the fisher lady said that there is a layer of liquid water on top of the ice, under the snow cover. That is not good for skiing, for the water will freeze to the bottom of skis, making skiing more heavy and clumsy. Instead of heading to the wide open lake I decided to follow the shoreline, and then find a way back home through the woods.

When I switched from the lake ice into the woods there was only something like 45 minutes to the seminar. I thought I'd make it back home in half an hour. Skiing in untouched snow was a lot of fun, the forest was beautiful with all the snow-covered trees, some of the treetops glimmering in sunlight. I haven't been so many times in that exact part of the forest, but estimating the directions I easily made my way to familiar places. There is that huge boulder which is split into two pieces. And that electric line. Down this hill and there is the place where I go pick lingonberries every autumn. And after that it is just that one uphill and then an easy route home. On I went, enjoying every moment of it; the fresh air, the quiet peace of the winter forest. And then suddenly I realized that I don't know where I am. Looking around the terrain was not exactly familiar. I paused to re-align my directions, estimating South by the location of the sun. "OK, I'm probably bit more to the North than I was aiming for. But, no problem, going consistently to the East will take me back to the easy route home."

A sense of adventure! At that point I was already feeling my muscles slightly strained, and under my warm winter clothes I was sweating. I kept on making my way through a snowy thicket, up a hill, under the arching branches of old big trees, in untouched snow where the only other signs of movement was the occasional tracks of a hare or a fox. The seminar was about to start. I sent them a message telling that I'll join in as soon as I get back to my home. Sunlight in pine tops. The sound of my own heart beating. Another uphill and - hey, I know this place! Seems like I had made a detour, almost a half-circle first going too much to the North and then correcting it a bit too much to South-East when strict East would've been better. But, no problem. I was a little bit tired and starting to get hungry, so I couldn't ski very fast, but at least I made it nicely back home. At home I set up my phone for the remote audio connection, and started to heat up leftovers for a meal. I had missed most of the presentation, but was able to participate in the discussion which was nice.

And the article? It was about the philosophy of mathematics, which I know very little of. Turns out that there has been some sort of debate in the field, about two different ways of mathematical reasoning. Namely, the computational and conceptual approaches. The computational approach is roughly the kind of mathematics you'd study at school - when you solve mathematical problems by crunching numbers. The conceptual approach isn't about finding an algorithm and then placing numbers for x and y. Instead, the conceptual approach is about defining or re-phrasing the given problem in such a way that the solution becomes evident. (Okay, I know, this is a huge over-simplification, but I decide not to explain it better here, for otherwise I'd end up writing another 18 pages of an essay). The thing is that sometime in the past the conceptual approach was a big thing, it was seen as "the new paradigm", the "right way of doing mathematics". Hehe, yes: 2+2=4, no matter if you approach it in the computational or conceptual way, so in that sense the both approaches are "right". So, apparently, a lot of thinkers interested in the philosophy of mathematics have been considering conceptual approach as "superior", "more advanced", or "more yay!" because it is elegant, intellectual and has some strange kind of charm in it. Then came the computers, and the computers quickly developed to be more and more efficient in doing mathematical calculations. And you know which approach a computer uses? Yes, I guessed it correct - the computational approach is what a computer does. A computer has no concepts to define or to frame a problem; a computer just blindly calculates what it is told to calculate; places numbers for variables x, y, z1 and z2 and z3....57832052 and then spits out a result faster than a human can write "let x be 1024" with a pen on a paper. So, even though the conceptual model was once considered to be a revolutionary new paradigm, the new "right way" of doing mathematics, somehow we have ended up in a situation where a lot of computational mathematics happens, and is standard applied method of doing science. Is that a problem? Does that pose philosophical questions?

In the article Fillon doesn't take sides. The main argument is that each approach has their uses, and the "right way" of doing mathematics is to choose a tool according to your needs. A lot like one of my own favourite analogues; if you are fastening screws the smart thing to do is to pick a screwdriver, but if you have nails then you'd probably better pick a hammer. And when reading the paper most of my own thoughts were hovering around these themes. Like, mathematics is often considered to be the field where opinions don't matter : three minus five is minus two, no matter if you like it or not, and you can't quite argue with the numbers. Mathematics is universal, and doesn't depend on the situation, culture or background - or at least this is what we like to think. 2+2 = 4 was true When Socrates walked down the streets of Athens, and the exact same equation was equally true when Confucius had a position in the bureaucracy of the State of Lu. And then, even on that field of Universal Truths the human mind is capable to invent a rivalry of two (or more) opposing styles, brands, breeds, movements, approaches or schools. I think this has very little to do with mathematics itself, but tells us something about the way human mind works.

Now, let me repeat that regarding those two styles of doing mathematics Fillon doesn't take sides. Neither is he neutral, disinterested, or opposing both of the styles. He simply just states that the tool x is good when you need to solve problem X, and tool y is good when you need to solve problem Y. And that some wisdom lies in the ability to see and to understand the proper uses of each style. I wonder what that would mean if the use the same analogue when it comes to things like politics? Like, let us imagine that there would be a country which had only two main parties (which, if you ask me, is a sad way of doing politics. When you have more parties, each party actually needs to do diplomacy, to listen to the opinions of others. But that is another story, maybe more about that in some other post). The human mind is tempted to start a fight over "our way is better than your way!", and then it all just degenerates into a petty race to power, the fight over "who gets to decide things". But, really - is hammer better than a screwdriver, or the other way around? Or what if we had an ability to calmly consider different situations, different needs, and different ways of solving this or that problem, and then deciding that "okay, for this particular case we are going to need some screwdriver over there, and then a little bit of hammer up there - but in that other case it is all just hammering nails, and for that third case the screwdriver is the optimal tool". After all, the ability to adapt to different situations is what makes us humans, right?

Okay, but the seminar discussion wandered on wide spectre of topics. For example, we were also pondering if computers will one day be advanced enough to do conceptual mathematics. And if that happens, would that then be a true revolution and a paradigm shift in mathematics? And could we, as embodied humans, understand the concepts invented by computer AI? Oh well - that, again is a topic easily worth 18 pages of an essay. Maybe later, in another post =)

lost in the woods - and happy about it =)
lost in the woods - and happy about it =)
312 users have voted.


Your trek through the forest was so magical, thank you for that Erkka! And I loved the discussion of mathematics, something about which I am so dim but always interested in. Great!


Yes I wish I'll have time for more skiing treks in the woods, before the spring comes. And maybe to post more pictures and stories of skiing in the woods =) Okay, the next time I'll ski to see that big split boulder, just to post a picture about it, although it won't be easy to capture with a phone camera.

And, mathematics, yes - how often it is used as an example of field of thinking which is supposed to be cold, hard, non-personal, universal, free of all dispute. And then when we take a closer look we find different schools having a heated debate on "our style of doing mathematics is better than your style, even when both styles yield the exacts same results, but hey let's just have this fight for the sake of having a fight!!?!" (Okay, I'm exaggerating a bit, just to illustrate this strange habit so often encountered in groups of humans.)

Hey Erkka, sure glad to see a big smile! That's a great pic! Sadly, I am jealous of your adventure which you had so close to home. We had a mm of snow a couple days ago, somehow I don't think I'd make it far. Our winter adventures consist of going to the closest city park, to see the same squirrels do the same thing they do the rest of the year.

The philosophy of mathematics. I think you're definitely on to something. This debate about who does the more correct math style exposes a certain human weakness. Of course it is good to debate things which need debating, but humans tend to gravitate towards conflict in a self destructive way. One part of our brain could even be yelling at us that it is pointless to be arguing this or that.. but still we let our ego get in the way.

Anyways, I'm not awake and shouldn't be trying to write about philosophy. I just want to say that, instead of debating what you've said, I totally agree! haha


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