Mathematics Corner …

… is the name of a regular mathematics column published online as part of The Citizen Scientist, which is a bi-weekly publication of the Society for Amateur Scientists. As part of my regular web-surfing today, I found the 15th October issue which is a new beginning for the column (after around six months of silence) and sounds like it might be worth following for those of us who are keen to learn maths.

This issue contains details of the various areas of maths and includes substantial lists of recommended books in those areas – some of which are freely available online. It concludes with a promise to start exploring the Riemann hypothesis with an assumed background of only high school algebra and geometry.

Heroes

Who are your heroes? The people you look up to, admire from a distance or aspire to be like. Do you have heroes? If so, are they famous people or “normal” people? These are some of the questions that have been running through my mind since listening to a Toastmaster’s speech given by my father on the weekend.

The first names that came to my mind were mainly sportsmen and women – cricketers, footballers, Olympians. I love watching sport, and I get the greatest enjoyment out of watching how people of similar skill levels perform quite differently in pressure situations. I believe sport at an elite level is a mental game – most elite sportspeople have the skills required – it’s just a question of who has the mental toughness to produce those skills when needed. Watching people produce their very best under extreme pressure encourages me to think that I, too, can do it – not in the sporting arena, but in life in general – I just need the right mental attitude.

Then I thought of my grandad – and particularly of comments mum had made after she spent some time in his hometown just before and after his death. She was surprised at the number of people who had stories to tell of how he’d helped them out – mainly just little things, but they’d been greatly appreciated. He was someone who shared himself with other people – his resources, abilities and time.

There is another group of people who have my admiration – they are those folk who are able to take everything life has thrown at them, and still come up with a smile and a positive attitude to life. The people who when they are diagnosed with a serious illness don’t say “why me?”, but say “why not me?” and get on with fighting it. Those elderly folk at church who, although they have many struggles with health, finances, etc, are always ready with a smile or a hug. People who can find the silver lining in any cloud.

There is a danger in having heroes, though, that was mentioned in a sermon a few weeks ago. Someone went up to Dorothy Day (a Catholic activist) and said how much they admired her, that they considered her to be a saint. Her response was quite blunt and challenging – basically she said that you consider me to be a saint and by doing so, excuse yourself from doing the things I am doing. If we regard our heroes as in some way superhuman and put them on too high a pedestal, then their actions no longer inspire us to be the best that we can be, but excuse us from making the effort.

Maths, finally

So, this week I finally got back to the Maths – I did a deal with myself that if I at least started on finishing off the Year 11 stuff, I could also start on the Year 12 book. So I have now sent in the final two tutorials for Year 11, and done revision notes for one of the four chapters I still have to do – then there is an assessable assignment and an exam to finish it all off.

The revision notes I have done were on the chapter introducing limits and differentiation. An interesting thing is mentioned which also struck me when I first read it – did you know that the rate of change of the area of a circle with respect to its radius is the circle’s circumference (A = πr² and dA/dr = 2πr) – and also that the rate of change of the volume of a sphere with respect to its radius is the sphere’s surface area (V = 4/3πr³ and dV/dr = 4πr²). I have no idea whether that has any real significance but it struck me as interesting (and a really good way of remembering the formula for the surface area of a sphere).

And, after all my hopes that at least now I’m working out of an official textbook, I wouldn’t have to contend with all the bugs, the answer given in the back of the book for the third part of the very first question in chapter one is - you guessed it - WRONG. Luckily the question is so simple that it’s very obviously a wrong answer, but it’s still a bit annoying. Once again, I ponder a career as a proofreader ….

Philosophy Gym

Tonight is the third meeting of the Philosophy Gym discussion group that we (the pastor with prompting from me) started recently at my church. The meetings are loosely based on selected chapters from the book “The Philosophy Gym – 25 Short Adventures in Thinking” by Stephen Law.

So far, we’ve looked at ‘Where did the universe come from?’ and ‘But is it art?’ – tonight we tackle ‘Is morality like a pair of spectacles?’.

According to the book, there are four options available to answer the question ‘what is the ultimate cause or origin of the universe?’:

1. Identify a cause;
2. Say it has a cause, but we can’t or don’t know what it is;
3. Say it doesn’t have a cause, it just is; or
4. Claim that the question doesn’t make sense (like asking ‘what is north of the North Pole?’).

All of these options have their faults from a philosophical viewpoint. I guess one of the reasons I have for wanting to study physics is to delve into questions like this from a scientific viewpoint.

The second session on art was quite interesting, too – with questions discussed like ‘does art require a human creator?’, ‘does art have to be appreciated by a human in order to be art?’, ‘is computer-generated art / music really art?’, ‘can there be a universally accepted definition of art?’.

Tonight we talk about whether things or actions are good/right or bad/wrong in and of themselves, or whether ‘goodness’ and ‘badness’ is something we impose on them from outside. My initial instincts are that we impose morality from the outside according to the inbuilt morals we have each absorbed from the culture we are part of. How else can we explain the different ideas of morality that exist within different cultures?

Broken promise

On Friday, I promised myself I would go back to the maths – it’s now Tuesday and I haven’t done it yet. I’ve really been struggling with my health for the last few weeks (I have CFS/Fibro) and my body has decided that it's time to rest for a while, and much as I might like to argue the point with it, that is one argument which I always lose in the end.

So, I’ll be spending some time doing a bit of web surfing, TV watching and generally lazing around trying to relax and not get stressed out by all the things I think I should be doing.

As part of the web surfing, I now have quite a few blogs which I visit regularly. Having found Electron Blue, which I mentioned earlier, I started checking out the blogs on her “other people” list, then following their links to other blogs, etc.

I found two blogs being written by people in the physics area at the University of Queensland, which would be my university of choice if I ever get healthy enough to attend a university. Michael Nielsen is a physicist working in quantum information science, and Joel Gilmore who writes Illuminating Science is a postgraduate student in the physics department. If you’re at all interested in physics or science in general, check them out.

Bookshops and procrastination

Each month, I allow myself one visit to a "significant" bookshop - ie one where I am seriously likely to spend money. Lately it has been the charity bookshop which sells the books that the Brisbane City Council library has removed from their collection - from which I have obtained some great books at awesome prices (like the 1994 edition of the McGraw-Hill Concise Encyclopedia of Science and Technology for A$2.50).

Today I found a new (to me) secondhand bookshop, which will no doubt be re-visited. I found it after making half a dozen phone calls to bookshops this morning looking for one which sold Analog Science Fiction / Science Fact magazines - it seems that most Brisbane used bookshops don't bother stocking secondhand magazines of any sort nowadays. I now have 11 magazines from the 1980s full of "hard" science fiction stories to peruse (and the knowledge that there are dozens more which are even older still sitting on their shelves).

I also found a book called The World Treasury of Physics, Astronomy and Mathematics, which is an anthology of modern science writing, including authors such as Richard Feynman, Albert Einstein, Werner Heisenberg, Max Planck, Isaac Asimov, Bertrand Russell, Roger Penrose, Stephen Hawking, Edwin Hubble, Steven Weinberg, Benoit Mandelbrot, James Gleick, Alan Turing, John Archibald Wheeler, Paul Dirac, C P Snow, Thomas Kuhn, Karl Popper, etc, etc, etc (ie lots of people that I've heard of). As well as the expected articles on physics, astronomy and maths, it includes articles on philosophy and science, and also about the scientists' lives and works. I'm hoping that dipping into it occasionally will help renew my flagging morale and energy when I get stuck in my maths and physics studies, and remind me why I'm doing this.

And yes, in case you were wondering, as of today, I have spent the last two weeks actively avoiding trying to write summary notes of the last maths book I completed - it's the last of four that were written in-house by the college through which I'm studying, and it's so riddled with mistakes (especially the chapter on statistics) that I'm really going to struggle to make enough sense of it to write useful notes. Once that's done and I've sent off the tutorial assignments, I have a test to do and then, assuming all that goes OK, I need to register for the first exam. Then I will have completed the equivalent of Year 11 Maths B in Queensland (we have 12 years of high school here).

Luckily the Year 12 Maths B is done using one of the textbooks that the schools use, so I should no longer be tripping over mistakes in the book all the time - although I admit to some fears over the Physics course, which I hope to enrol in sometime in December or January, which is written completely in-house.

Tomorrow, I will go back to the maths, I promise – that is, unless I find something else more interesting to do, or I’m too tired, or I get distracted, or ………….

Conceptis logic puzzles

They say confession is good for the soul – and also that the first step in overcoming an addiction is to admit you have a problem. Well, I have an addiction to Conceptis picture-forming logic puzzles (Warning: click through to their site and you, too, may become addicted) - although I’m not at all sure I want to do anything about it.

Each week they post 12 free puzzles for registered members (registration is free) which can be completed online or downloaded and printed. The puzzles are of three types – pic-a-pix (otherwise known as nonograms or paint-by-numbers puzzles), link-a-pix (the easiest of them, I think) and fill-a-pix (which are my most serious addiction). There is also an active forum community and a weekly puzzle to download and review, with one of the reviewers each week receiving a free t-shirt (look under Puzzler’s Place once you’ve logged in).

For more months now than I care to admit (or should it really be counted in years?), one of my high priority tasks for the week has been to complete all 12 puzzles. I often put my computer on standby overnight so that I don’t have to close a partially completed puzzle and lose it all. Just a hint for anyone who does try them – you don’t have to be online to complete them – log in to the Conceptis site, open a puzzle and then just make sure you keep the web browser window with the Conceptis site on it open, as well as the puzzle window.

Just don’t say that I didn’t warn you that they’re addictive ………

What our leaders believe

That was the title of the latest episode of Compass which aired on ABC television in Australia last Sunday. Compass is a series “devoted to faith, values, ethics, and the religious impulse in today's world” to quote from their home page. This episode consisted of interviews with the leaders of the major political parties in Australia about their values and belief systems, done in the lead-up to the Australian federal election this Saturday (for a complete transcript see here).

I find these (potentially) less formal, less political interviews to be far more useful in uncovering the real men (and yes, they are all male at the moment) behind the media “mask” than any other means.

A few years ago, prior to a previous election, Ray Martin did what were intended to be personal interviews with John Howard and Kim Beazley, the two contenders for Prime Minister at the time. I remember being struck by how “real” Mr Beazley seemed – just “a bloke having a chat”. In contrast, Mr Howard was still very much the “politician” – every word seemed measured and designed to fit in with the “image” his PR people wanted him to portray.

This time, five leaders were interviewed, and again, Mr Howard stood out as the only one who was, to some extent, still being the politician – that was my impression, anyway - he seems to be a very private person when it comes to his personal beliefs and values.

The others were very interesting. One thing that really struck a chord with me was John Anderson saying that one of the things we lack in Australian society is a “story”. I came across this concept of a story or meta-narrative earlier this year – a story which tells us who we are, what our role is, what the universe is and how we should act. The obvious examples come from organised religions such as the Christian story of the creator God.

But as society moves into the post-modern era and tends to shun organised religion, we also leave behind our story. So we find people who feel lost in the world, who don’t know who they are, why they are here or what the world is all about. I wonder whether science can provide us with a story that helps – that goes beyond the Big Bang, evolution from apes, etc, and somehow helps us find our place in the world. I believe that we need a story that incorporates scientific knowledge as well as spirituality in some way.

An inquiring mind?

I pondered long and hard over naming this blog – I wanted something that somehow reflected who I was, but that left plenty of scope for exploring my wide and varied interests.

As a young child, rumour has it that one of my first words was “what?”, closely followed by “why?” – mum tells stories about me following her around asking “what you just doing now, mum?”, “why you just doing that?” and “what are you just going to do next?” (and no, I don’t have any idea where the “just” came from).

Starting school was something I eagerly anticipated – somewhere to find out the answers to all my questions. But, that wasn’t how it worked out, as I quickly became caught up in the quest for better and better test and exam results. The insatiable drive to understand things was consumed by a need to be perfect, to know everything I was supposed to know, or at least to know it well enough to be able to perform when tested.

There were glimpses of my former self – the chance as a primary school student to spend half a day a week at a high school learning (among other things) to build a crystal radio and to program a computer (using punch cards – ok, so I’m in my forties, and it was a while ago) – and a high school maths teacher willing to spend some of his spare time teaching me some of the interesting maths and physics that wasn’t in the curriculum – and who gave me a large book called “Physics for the Inquiring Mind”.

But I found myself going fairly thoughtlessly from high school on to university, just as everyone expected me to – studying maths, computing and science subjects – but still only really motivated by the need to excel at the exams. So, when I got married at the end of second year university and started struggling to combine married life and study in third year I found it relatively easy to drop out and leave the academic world behind me.

And so I went on, through a divorce, getting myself a government office job, a computing qualification, a better government job, a move to sunny Queensland and yet another government job. Then, in late 1997, I was diagnosed with fibromyalgia and chronic fatigue syndrome and had to stop working (I was later retrenched from my job and I haven’t worked since).

I found I had lots of time to think, to ponder my life, and one day, several years ago, to pull Stephen Hawking’s “A Brief History of Time” out of my bookshelf where it had sat unread for years and actually read it. And I remembered that part of me that wants to know why things are the way they are, how things work, the “me” who just has to ask “why?”. So now, I have a slightly larger collection of (as yet mostly unread) popular science books, and I’m enrolled in a self-paced distance education course revisiting high school maths and science. And one day, the dream is to understand modern physics – and all the maths involved – to be able to read the newsgroup sci.physics.research and have at least some of it make sense.

The dreaded first post ...

... and this time for real - cos I've deleted the test one that's been sitting there for a few days while I fiddled with adding comments, trackbacks, permalinks and a site counter - some of the stuff the "experts" say you should have - which hopefully all works ok. But now it's time to stop wasting precious hours trying to figure out how to edit the HTML code to put an extra space or two between the time and the "LINK" in the "POSTED BY" line below (suggestions for fixing it welcomed by this HTML novice) - and get on with actually writing something.

I've also spent some time reading all those lists of do's and don'ts for beginning bloggers, so hopefully my blunders won't be too big - although I am a firm believer in the premise that the best way to learn is by making mistakes, even if it is scary.

So ... why am I doing this? I started reading a couple of blogs a month or so ago - I'd heard about the whole blogosphere thing before but never explored it properly. At the time, I was curious to see if there were any other "laypeople" who were trying to learn maths and physics (in particular) by themselves, and my search revealed Electron Blue - Pyracantha's weblog, subtitled "an artist studies mathematics and physics". I read that from start to finish and followed lots of links to other webpages and blogs - and I was hooked.

I spend a lot of time exploring ideas, gathering information, reading books and surfing the web. I've always liked the idea of keeping a journal or record of life in general and my "thought life" in particular but have never been disciplined enough to stick with it. My hope is that by blogging in a public forum I will develop the habit of crystallising some of my random wanderings and retaining more of the lessons I have learned - and who knows, someone out there might find some of it worth reading and even learn something, too.