Funes the Memorious

At least once a year my thoughts turn to Ireneo Funes. The first few weeks of Access Maths mostly deal with topics I think people should already have met: basic algebra and trigonometry, logs, etc. After this the tone of the course gets more grown up as we start to discuss sets and functions and it's at this point that Borges' story, Funes the Memorious gets a mention.

Funes is a most remarkable man, superhuman in some respects, proto-human in others. He has perfect memory and remembers every sensation he has ever experienced but these hyper-detailed recollections torment him and he suffers from chronic insomnia. To mitigate his insomnia he sets himself nocturnal projects, one of which involves giving every (whole) number a unique name. "...in a very few days he had gone beyond twenty-four thousand". This is a completely crazy project, of course, "precisely the contrary of a system of enumeration" and requiring an infinite length of time for its completion. It makes a charming footnote, completely optional as such footnotes are, to the introduction of the natural numbers.

Consistent with his perfect recollection of every experience, Funes is almost incapable of abstraction. He would struggle to understand why the word, "dog" could apply to both a Scots terrier and an Irish wolfhound. If each object we meet in the world is unprecedented, why would we even need numbers at all? They could become a game of the sort that Funes plays.

It's typical of Borges that a story of just a few pages should contain such rich, deep ideas. The story was first included in the collection, Ficciones, translated in English as Fictions, and can be found in other collections. I think the first translation of Fictions was published in 1962, so these stories are probably still copyrighted. I will leave it to you and Google if you want to try to find a free copy online.

Last Thursday, discussing functions, I wanted to underline the idea of "dummy variable", that we use a letter like f to stand for a function, not its value or its operation, and that once we have temporarily introduced a symbol, e.g. x to stand for "the number we are going to give to f", we don't really care about x again after that; x is just a placeholder and we discard it once it's done its job, of explaining how the function works. So we can write, e.g.

f(x) = 2x-1

but then ask, what is the value of f(2), f(-14.7), f(a), f(p²), etc. We can even suppose that a more modern Ireneo Funes has chosen to call one number, Bobdylan and write

f(Bobdylan) = 2*Bobdylan-1

We supposed that Bobdylan was Funes' name for 17. Then the result of this operation would be 33. From the class came the suggestion that Funes would have named 33, Batman. So we were able to write,

f(Bobdylan) = Batman

Of course there was a reaction: "Please leave that on the board for the next class."

Some reasons to be cheerful

My wife and children. Close friends and family. People in whose house you're always welcome just because you're you, irrespective of successes or failures, good deeds or bad, even if you've been a shit, a disappointment to the decent, a source of pain. Beyond those:

• Landau and Lifshitz course of theoretical physics
• Borges Fictions: Tlon, Uqbar, Orbis Tetrius; The Approach to Al Mu'tasim; Funes the Memorious;... Here's a Borges eulogy; no such article can really reflect what these stories do in the head of any individual reader.
• cask strength single malt whisky
• Paul Bley
• Consume Red
• Diamanda Galas
• Cardiacs (this song is so fantastic, it shouldn't be freely available like this. Go and make the world a better place to say thanks because you could listen freely to this. And buy the CDs)
• Trout Mask Replica; Mekanik Destruktiv Kommandoh; Red
• Keith Tippett
• random Glasgow people, don't even know their names mostly
• horizons as the Sun goes down
• Ito calculus

That'll do for this evening. More next lifetime.

Drunk

I don't get drunk any more. Or maybe if I do, it doesn't make any difference. When I did get drunk I had a favourite conversation: "what was the greatest gig you were ever at?" How vulgar. Next time I get drunk the conversation will be, "what was the greatest gig you weren't at?" Probably this one.

Only sky

Only sky is what's in this picture (and a little sea). I took it at Westport. Look west from Westport and the sky stretches to Newfoundland.

Only Sky is also the title of a very beautiful record by David Torn; one man, electric guitar and oud, an effects rack and a deep musical sensibility. It's always good to look up.

Books

I've been reading books. Always dangerous.

In The Corporation by Joel Bakan I found ideas like this:

As a psychopathic creature, the corporation can neither recognize nor act upon moral reasons to refrain from harming others. Nothing in its legal makeup limits what it can do to others in pursuit of its selfish ends, and it is compelled to cause harm when the benefits of doing so outweigh the costs.

Joel Bakan is a Professor of Law at University of British Columbia, no ranting hippy. This view is substantiated in detail via a historical review of the emergence of the corporation, an analysis of the legislative framework defining the corporation, and detailed accounts of particular legal cases. Reviews said things like, "...a surprisingly rational and coherent attack on capitalism's most important institution."

Before picking up The Corporation (and alongside books on quite different topics, and again quite different topics) I had been looking at Neoliberalism: A very brief introduction by Manfred B Steger and Ravi K Roy. For the last few decades much of the world has been run in a certain way associated with the names Thatcher and Reagan, Blair and Clinton. The word, "Neoliberalism" denotes an attempt to define the key features of this project. Again, a quotation:

Neoliberal modes of governance encourage the transformation of bureaucratic mentalities into entrepreneurial identities where government workers see themselves no longer as public servants and guardians of a qualitatively defined 'public good' but as self-interested actors responsible to the market and contributing to the monetary success of slimmed-down state enterprises.

So, we convert the instruments of state - health, social services, education, regulatory bodies - into the same sorts of "psychopathic creatures" that dominate the marketplace. They will operate in a landscape defined partly by income and expenditure, exactly like companies; but also partly by "targets" and "Key Performance Indicators", instruments of management put in place with the intention of ensuring they continue to meet their societal purposes (here's a pretty grim account, not at all reassuring of this process in UK higher education). We are apparently confident we can do this in a way that will offset any psychopathic tendencies they might start to display. Good idea?

Cycling in the universe

I went out on my road bike, first time for a year. Heading south down the A77 I did not feel awful, stronger than expected. I kept going. I turned the corner onto the Eaglesham Moor road and discovered a fierce headwind that had previously been behind me. Oh dear. The steepest climb of the outing became even more gruelling.

At the top of the Eaglesham Moor road there's a layby. I stopped there for a minute to recover. A strong, experienced looking cyclist arrived from the west, same as I had, saying, "that was awful!" In principle this is a drab, empty spot but it always seems really beautiful when you've attained it solely by your own efforts, starting from the populous suburbs. On a clear day there is a very open view west with Arran in the distance. It's even more uplifting if you arrive from the east so that the vista towards the coast suddenly opens up after a bit of a climb.

How does one deal with a climb into a headwind, when the unfeasibly slow pace does not seem to justify the pain? Head down, lowest functional gear, stop looking around, keep pedalling. My thoughts turned in, away from the wind. Would a lighter bike help? I never indulged my cro-mo longing but it did provide some raw material for a blog posting. I'm still on the bike I owned then. Its frame is aluminium. Like almost all other chemical elements aluminium was synthesised in nuclear reactions during the life histories of stars. It exists on Earth now because of events that took place in the insides of long-dead stars - BIG stars, more than eight times the mass of the Sun. Our poor little Sun will never see such events but it will see a stage in its life, far in the future, long after it has swollen up until it engulfs the Earth, in which carbon is manufactured in its deep interior. Carbon might be even better for bike frames than the cro-mo alloys, very light, super-strong yet forgiving for the rider. There's lots more carbon lying around than molybdenum - got manufactured in many more stars - but the production of carbon fibre and the manufacturing process mean carbon bikes are even more expensive.

And what's the deal with this stupid wind anyway? Sunlight falls more obliquely on the ground in the polar regions than at the equator, so the air is hotter and the gas pressure greater at low latitudes so air starts moving. Mix in the rotation of the Earth, variable cloud cover, friction with the ground and the shapes of the land masses etc. and before you know it you have a messy, changeable weather system. Another aspect of everyday life that finds its ultimate explanation in Earth's place in the cosmos, exposed to light from the Sun.

In so many ways my bike ride, like all of our existence - pleasures and headwinds! - couldn't be what it is without our place in a huge, old universe.

York

Wallowing in that ineradicable streak of Adult Educator I attended the annual meeting of UALL, the Universities Association for Lifelong Learning. (Of course I'm being a little flippant; I'm currently Vice-Chair of UALL's Scottish wing, SUALL). I heard presentations on topics like older adults learning (how, why do people really learn in their 80s and 90s?); patterns of learning, and indeed life more broadly, in cities; "work-based" learning (which might be a way into work as well for people in work), etc. Some of them were more relevant than others to details of my own work but all had some interesting ingredient. I particularly enjoyed hearing from some of Leeds' Learning Champions, mature students who are happy to act as advocates, to tell their "I did it, so can you" stories to people who might be thinking of study themselves. We have a lot of these stories among our own Access students and I was left wondering if we might start something like our own Learning Champions scheme.

My professional identity has been sliced in two. For half the week the Access programme gets my attention and I'm an adult educationalist. In the other half I'm an astrophysicist, teaching and researching. At the UALL conference I wasn't thinking too much about Astronomy but that changed suddenly and unexpectedly.

The weather was kind: brilliant sunshine, azure skies, but cold air, especially in the low late afternoon Sun. I sat on a bench in the Dean's Park replying to email (eduroam seems to work throughout much of York city centre). Walking along Minster Yard I was already a couple of steps past this plaque when the name "Goodricke" sank in. When the deaf and dumb John Goodricke (1764-86) died at the age of 21 he had already made a lasting mark on Astronomy. People who only ever glance casually at the sky will find the stars unwavering. They might be surprised to learn that many of them vary significantly in brightness. Goodricke made some of the earliest discoveries of such variable stars, in particular the star Algol, in the constellation of Perseus. Every 2.87 days Algol drops to about a third of its normal brightness. It takes a few hours to fade to faintest, stays more or less this faint for a couple of hours, then brightens up again over the next few hours. This is easy to watch, once you know to look for it, and predictions of the times of minimum brightness are available online. Together with his pal Piggott, Goodricke correctly guessed the reason for this regular fading: the eclipse of a bright star by a fainter, orbiting companion. Here's a nice discussion of this famous star, just one more point of light to the casual eye but beautiful in its regular behaviour.

I was jolted out of my adult educator identity into my astronomer identity, a bit like those moments at the end of each episode of Quantum Leap when Sam Beckett finds himself in a different body, in a new time zone. The memories that popped up, however, were from the time when I was neither one thing nor the other but a true hybrid: an adult student, outside the Paisley Coats Observatory many years ago, saying out loud, "that star's really got brighter since we started watching"; a student on the BEd course, training to be a primary school teacher, whose project report described a very cold winter night camping on Rannoch Moor, popping out of the tent every 20 minutes for another Algol brightness estimate. Ah, the were-astronomer days.