Mathematics: Two Public Lectures (Oct 2005)

Subjects: Ramanujan; Applications of Mathematics.

On Thursday (27 Oct 2005) I attended a lecture at Sydney University about The Life and Notebooks of Ramanujan. Ramanujan was an Indian mathematician who worked in England with the famous G. H. Hardy during World War I, and he ranks among the most intuitively brilliant mathematicians ever to have lived; probably the greatest. Merely to hear or read of his achievements is inspiring. In the lecture we learned:

• He grew up in the southern area of India, showed incredible interest in and aptitude for mathematics by the age of 12 (by devouring an advanced university-level text and answering all its problems).
• He loved calculus and hated geometry, and ignored non-mathematical subjects, causing him to get a poor mathematics mark and fail most other subjects at university.
• He worked in isolation on a piece of slate, economising on paper, which was expensive, by recording only his results (i.e. without proofs). He was confident that he could reproduce any of the proofs from memory or intuition. I think I’ve read that he didn’t place great value on proofs – which Western mathematicians and probably most others consider essential – but perhaps this isn’t true.
• He wrote to a few English mathematicians with about sixty of his results. Most foolishly ignored him; Hardy recognised potential genius and wrote back asking for proofs. Ramanujan wrote again without proofs but with another hatful of results!
• He travelled to England to work with Hardy, against the precepts of his Brahmin doctrine, but with the eventual blessing of his mother. Despite this supportive act, she was in some ways a shrew, blocking contact between him and his wife while he was away.
• His time in England was mathematically incredibly productive, but deleterious to his physical and mental health. The privations of war made it impossible to satisfy his diet, and his loneliness in a foreign land accelerated the illness that killed him in 1920 aged 32. If you can imagine Einstein being killed in his prime, you can imagine the impact of Ramanujan’s illness and death on mathematics.
• While working “publicly” by publishing papers with Hardy, he worked “privately” by recording results (again, no proofs) in a series of notebooks. His life’s work apparently consists of over 3,000 proved theorems, so that sounds separate from his notebooks. The notebooks probably began before his work in England, because they are two-thirds original. I.e. by working in isolation, he “discovered” much mathematics that was already known by others. Anyway, his notebooks are an inspiration for current mathematical research nearly a century after their writing.
• Ramanujan’s wife (whom he married when she was 9) died in the 1980s aged 94. The lecturer visited her once or twice and determined some threads from her life. She worked all her life sewing clothes, if I remember correctly, and despite being very poor gave away half her income to charity.

The man delivering the lecture (insert name here) has spent 20 years, with the help of PhD students, integrating into mathematics the contents of … wait for it … one chapter of one notebook. By “integrating”, I mean finding proofs for the results that Ramanujan wrote down.

The lecture included many photos but, sadly, very little mathematics: this was one of several lectures he delivers on Ramanujan, so the mathematics is obviously presented elsewhere. The lecturer strongly recommended the book The Man Who Knew Infinity for more information. In fact, reading the reviews of that book on amazon.com is likely to be more educational than reading this blog post. I'll certainly read the book if it contains some insight into his mathematics.

The second lecture was on Friday 28 Oct 2005 at Macquarie University. Bob Anderson of CSIRO gave the sixth Moyen lecture, in honour of Joe Moyen, who wrote a very influential paper “Quantum Physics as a Statistical Theory”, or some such, in the 1940s. The subject of the lecture was Applications of Mathematics. It was entertaining and informative, with several sub-messages such as “In a crisis, you don’t rise to the occasion; you sink to the level of your training.” (I.e. it’s worth acquiring a lot of knowledge.)

Bob was delivering the lecture because he was awarded the Moyen medal for distinguished contribution to mathematics, physics, or statistics. He has clearly been involved in a lot of mathematical modelling in industry, and dwelled on the following examples:

• determining which grains of wheat are soft (good for pasta) and hard (good for biscuits);
• restricting the strings in the Stuart and Sons piano to vertical movement, thus providing a richer, purer sound than other pianos; and
• analysing the genetic geometry of cotton in an attempt to increase its yield.

All examples made use of sophisticated mathematical modelling to gain an understanding of the physical aspects of the objects under investigation. He convincingly demonstrated the importance of mathematics to these advances in technology, and aimed his talk at a reasonably general audience rather than highly-qualified mathematician. The only suggestion I’d make to Bob is to wrap up each example better, summarising the problem, the mathematics, and the solution.

An ulterior message was clear: significant technological advances can’t be made without people applying difficult mathematics to problems. That obviously can’t happen without lots of people being trained in mathematics, which makes the current decline in high-level mathematics study in Australia, both at high school and university level, rather alarming. It’s a problem that feeds on itself: less qualified mathematicians today means less (good) mathematics educators tomorrow, which means even less qualified mathematicians the day after. Once the impact of this problem becomes clear, it won’t be possible to ramp up production of mathematicians.

Perhaps that’s not a problem. Perhaps we have all the technology we need and can cope with declining research and development for a few decades, but I doubt it. The grain and cotton problems above are good indications of the problems we may face without such research: a reduced inability to improve farming and food production techniques in order to feed and clothe the world.

Book: Dirt Cheap

Dirt Cheap, by Elisabeth Wynhausen, is an Australian journalist’s record of her one-woman social experiment: to spend about a year in minimum-wage jobs and see if she can live solely on her meager income. I was immediately attracted to the book when I saw it at the library, but thought it would be recording other people’s experience rather than her own. While her experience is interesting, it’s not entirely genuine, as she does rely a little on her savings (she had little choice), and she is sometimes confrontational in the workplace, knowing that she’ll soon be leaving of her own will.

This experiment is not unique: it was inspired by a similar effort by an American woman, Barbara “Somebody”, and has been followed up by a TV show featuring Morgan Spurlock (of Super Size Me fame) doing the same thing for 30 days. I’m not entirely surprised that more than one person is documenting minimum-wage reality: despite all the information available to us in modern times, we’re probably less aware of how other people really live than we ever were. As Alain de Button told us in Status Anxiety, once upon a time everybody knew their place in life and accepted it. Now, with opportunity in theory extended to all, I think we tend to guard our life experience a little, as our friends and neighbours can seem to be our competitors in the rat-race of life. As work is the foundation of most people’s lives, if you don’t work with wage-slaves, you’re unlikely to know any. Of course, we all think our experience of life is more or less the norm, but of course it isn’t. Anyway, when I last worked in an office, I saw the cleaners doing their nightly duty and wondered what their life was like. I even conversed with a couple of them on the odd occasion, but of course never gained any real insight. Thus I’m grateful for Wynhausen’s book, and, though I haven’t consumed them, the work of “Somebody” and Spurlock as well. Many people would likely find themselves more grateful for their standing in life if they took advantage of these insights into the lives of others.

Turning to the book itself, I found it a compelling read. At about 300 lightly-worded pages, you can knock it over pretty quickly. It describes about six jobs she had, each lasting a month or so. She covered a lot of geography – two cities and a rural area – and paid for accommodation from her earnings. Occupations include: sandwich hand; an egg-packing factory; office cleaner; nursing home attendant; hotel breakfast attendant; checkout operator; and … that’s about it, I think. There are a wide variety of experiences with bosses, customers, and co-workers. The conclusion that each chapter seems to share is that the worst aspect of the low-wage existence is the lack of dignity afforded by employers: the low value placed on your time, convenience, and morale. Readers: when you deal with low-wage people in future, remember that they probably take crap from bosses, customers, and even workmates; do they really need to take it from you too?

It’s a book worth reading. I would, however, like to see a book that documents the lifestyles of genuine wage slaves, who lack the options Wynhausen could fall back on. One thing’s for sure, however: I’m less bitchy about the relatively low teachers’ pay I’ll be collecting next year.

John Simon on Criticism

Just a quick quote from Newsweek (September 26, 2005), in John Simon's piece Criticism in an Uncritical Age. Simon, apparently, recently published three volumes of his theatre, film, and music reviews. That such reviews are considered worth reading long after they were written is an achievement. His short piece in Newsweek examines the art and relevance of criticism in an age where everyone's a critic. Anyway, two quotes.

Like any self-respecting critic, I have always encouraged my readers to think for themselves. They were to consider my positive or negative assessments, which I always tried to explain, a challenge to think along with me: here is my reasoning, follow it, then agree or disagree as you see fit.

And later:

I have always maintained that a critic has three duties: to write as well as a novelist or playwright; to be a teacher, taking off from where the classroom, always prematurely, has stopped; and to be a thinker, looking beyond his specific subject at society, history, philosophy.

These are inspring words. I read lots of opinion pages in newspapers and magazines, and thoroughly dislike strong opinions being voiced without strong arguments being made behind them. (Opinion writers are merely critics of society, so Simon's words should apply.) Worthwhile critics invite the reader to disagree with them by laying out their reasoning instead of bludgeoning the reader with unrepentant ideology. The most enjoyable analysis of politics, policy, and society is sparklingly well written: enjoyable to read regardless of the content.

So thank you, John Simon; I'll look into your three volumes of reviews with pleasure.

Riot in Ohio

On the news tonight two black rallies were reported. One, in Washington DC, was a 10-year anniversary of a million-strong march. I don’t recall the original event, and don’t know anything more about it (yet). The news report highlighted one speaker decrying racism in America, and the reporter (unfortunately) linked this to Hurricane Katrina. Whether the speaker or assembled masses intended such a link I don’t know, but I don’t really doubt it.

The other rally was a negative and less planned event. A white-power group staged a planned rally, and a large number of black people revolted. It got ugly, with rampaging and looting; even a vehicle that looked like an ambulance had rocks hurled at it. The reporter said the conflagration really started when police, who didn’t do anything about the “illegal” white-power rally, arrested or perhaps just interfered with a black person who was reacting to it in some (presumably anti-social) way.

Now, what to say about all this? Firstly, the white-power group is a disgrace and deserves strong condemnation for its beliefs and its public display of them. Secondly, the contribution of the black crowds to an ugly situation is understandable. The anger would be real and justified. Thirdly, the spreading of that ugly situation to include the destruction of public and private property – the property of people who had nothing to do with the rally – is disgraceful, and a poor reflection on the black community in that area. The neo-nazis are human trash, but they are a tiny minority and represent noone but themselves. The black community that rioted, however, represent misbehaviour on a grander scale. Although it’s suspected that much of the damage was done by smallish gangs taking advantage of the situation, it was the actions of the entire mob, presumably, that allowed the situation to escalate. The worst thing is that this display of black power, as it were, is self-defeating, because it’s the exact response that the neo-nazi animals probably wished to provoke, as if to prove a point.

How should the community react to a white-power rally? Well, if it’s illegal, as the news reporter said, it should have been forcibly stopped by police. It’s understandable, if regrettable, that the black mob took matters into their own hands because police didn’t act. However, one can take a step back and consider a different response: ignore them. The Nazis want a response; the most frustrating thing for them would be to not have an audience. If the community could rally together, as it were, and show these scum that their existence is not worth noting, let alone reacting to, then perhaps that would be the best outcome of all.

The other option is to perform a John Belushi move a la The Blues Brothers, in which Jake and Elwood Blues were held up by the Illinois Nazis marching on a bridge. Messrs. Blues were in a hurry, and … if you haven’t seen it, you really must.

Note: this piece was written without access to the facts of the case, and offers a general opinion only. There were probably more factors at play than I’ve accounted for.

Richie Benaud, King of Cricket Commentary

Richie Benaud is 75 and still appears on Channel 9’s cricket coverage. His voice is weaker than it once was, but he continues to provide warmth, authority, and a soothing tone to the soundtrack of the Australian summer. As a mate of mine put it, he’s the only commentator who you never argue with. I think that’s stretching the point a little; there are two others whose words I greatly respect: Tony Grieg and (a recent discovery) Mark Nicholas. Further, during an Australia–South Africa Test match about 10 years ago, Richie let slip about the stupidest thing I’ve heard on television: “And here we have a kite … possibly motorized.”

An interesting facet of this great man (great player in the 1950s and probably 1960s; great commentator for decades) is his incurable old-school charm. He has an enormous amount of consideration for the person watching, wanting to be entertained by and informed on the great game. In two interviews I’ve read, he mentioned the great responsibility that comes with being invited into viewers’ living rooms. He spoke of the value of opinions he receives in the streets, despite the hassle of being so well known. And at the end of a radio interview recently, which I missed but which I gather was aimed at promoting his new book, he sounded most sincere as he thanked the host and her listeners. His modesty is his greatness.

It’s also his mystery. He lives a simple life, except that he lives comfortably in three countries (Australia, England, France), has a dream job, and has a cosy relationship with Australia’s richest person, Channel 9 boss Kerry Packer. Packer is a fierce, but fiercely loyal, employer, and will be genuinely grateful, not merely commercially grateful, at the decades of service Richie has provided.

I thought he was planning to retire a few years ago, and summer after summer have been relieved to find it hasn’t happened. It now appears he intends to keep going until he “falls off his twig” (his words), or his two career advisers (Packer and his wife Daphne) tell him it’s time to pull up stumps.

Mark Nicholas has shown public gratitude to Richie as a mentor in a newspaper column, and I think he’s the right person to front the next generation of cricket commentators. He employs the same economy of expression, highlighting the themes of the day’s play rather than the minutae. And his voice has a similar relaxing quality. The only problem is that he’s English: we’ve only heard him on Australian television because of Australia’s recent historic stouch with the old – and renewed – enemy. But if Richie made a career of following the summer between Australia and England to provide his expertise wherever it was required, I don’t see why Nicholas can’t do the same. There’s still a few years to pass on the baton.

Reason Magazine

I'm putting a permanent link to Reason Magazine on the side of this blog, because it's such an interesting read, and no-one I know has heard of it.

It's a US magazine that covers a range of issues in society, politics, and economics, with a libertarian bent, and always in a well-written, well-argued, and interesting style. The authors are all independent, and you'll occasionally find differing perspectives of the same issue among them.

I used to read The Economist, a more well-known UK publication, every single week for more than two years, and still have all the issues I bought. It's a terrific magazine, or "newspaper" as they call it, with a similar ideological slant to Reason, but perhaps more appeal to authority. I stopped because I could no longer afford to buy it every week, and the amount of text in each issue was kind of overwhelming.

Anyway, both publications provide a valuable service: a set of well-written and well-argued opinions against which to test your own. I commend them both.

Music: Jon Spencer Blues Explosion

Jon Spencer Blues Explosion is my favourite musical outfit at the moment. They dropped the "Jon Spencer" from the name for the latest album Damage, and I'll adapt eventually.

Their core style is a perfect meeting of rock 'n' roll and blues. Not the sad blues, but the drivin', jivin', dancin' blues. Guitar sometimes sounds like early Stones; vocals often sound like Elvis; but they're derivative of neither. The best of their music makes movement involuntary. It's about all I've been listening to so that I can wake up enough to plough through another day of uni assignments.

These are the four albums I have, in release order:

• Orange. Many consider this their masterpiece, but I consider it dated. It's raw, playful, energetic, but somehow shallow. Still a great album, mind you, but I don't play it often.
  
• Now I Got Worry. I consider this their masterpiece. The most bluesy by a long shot, with a great cameo from recently retired blues legend R. L. Burnside. Full of drive.
  
• Plastic Fang. Underrated, in my opinion. Not every song is killer, but none stink, and many are killer. What's more, it's their most consistent album in style, that style being full-bodied rock 'n' roll. When you're in the mood for it, it delivers a whole album's worth.
  
• Damage. Only got this recently and I'm still evaluating it. It doesn't grab you straight away, but has been warming on me. This is the "other" side of Blues Explosion, the experimental side. A range of styles on this one, but fortunately it includes some standout rockers.

They've got about nine albums in total, I think, and I gotta get some more.

I first got into this band in a pretty straightforward way: I bought Now I Got Worry simply because I liked the name of the band! The concept of blues exploding was one I could anticipate with relish. They certainly didn't let me down.

Introducing Midnight Rambler

Cool! Every time I add a post I'll have The Rolling Stone's Midnight Rambler in my head. Can't ask for more than that!

Midnight Rambler is a blog that will discuss music, words, education, mathematics, politics (not slanging matches), and other things as they come up. If there's an overarching goal, it's this: to document abuses of logic and common sense in public discourse.

If there are any readers, welcome. Drop me a line!