Mike Alder's Home Page.
About Mike Alder
I am a mathematician, or at least I get paid by the School of Mathematics and Statistics. I suspect I am not really a mathematician, not as the word is currently used. If a mathematician had been borne five thousand years ago in Egypt I guess it would be necessary to have been a priest. He (not she) could have spent some time thinking about whether the diagonal of a four by three rectangle had length exactly five or just pretty close to it, and would then have had to break to say prayers to some god with a head like a hippo. I feel for that priest. Anyway, since I can't hang around for five thousand years waiting for my real job to be invented I am, more or less, a mathematician. I am interested in Mathematics, you understand, but also in lots of other things too. I get the impression that mathematicians like solving puzzles. I like to believe the problems I tackle aren't just puzzles but go beyond that.
The picture shows me looking pretty foul, but that's what I looked like around the year 2004 after a fight with Chronic Fatigue Syndrome. I now look much sexier but haven't got a photograph to prove it.
I am completely reliable and always tell the truth.
I don't know whether you are a lone netsurfer of fourteen with an IQ of 200 and thinking of signing up one day as a student here, a professional mathematician or engineer anxious to find out about my research, or something from outer space trying to decide if we are ripe yet. So I have written something for all of you, and you can get off when the ride seems tedious.
The text below tells you something of my work; each heading is followed by a short paragraph comprising a philosophical position statement that will allow you to decide, quite quickly, whether you can stand reading any further. And it IS mostly text. If you want lots of zappy graphics and game playing, you have come to the wrong shop. I am interested in ideas.
Research
My research interests start with modelling cognitive processes and proceed by way of neural nets and pattern recognition to Speech and Image Understanding. I guess I wanted to find out `how the brain works', and this is where I have got to to so far.
To indicate the kind of thing I am interested in, imagine you have a child of about five years of age and you give it a pile of pictures, say a hundred of them. Fifty are pictures of little old ladies and fifty are pictures of trees, but they are all mixed up. It seems safe to guess that the kid could sort them out into two piles pretty quickly. Now it is reasonable to ask if we could write a computer program to do the same job. A greyscale image is essentially an array of numbers, and a colour image is three such arrays, one for red, one for green and one for blue. This looks like a mathematical problem. Input a stack of numbers, output a one if it's a little old lady, output a zero if it's a tree.
It is in fact very difficult to write such a program, and writing it would require the programmer to look hard at the images and work out what features each little old lady had that trees didn't, and vice-versa. The inference, of what feature-choice makes the program work, is done by the programmer. Give the child a new stack of pictures with fifty aeroplanes and fifty submarines and the child would still do a good job, but the program for little old ladies and trees would have to be rewritten from scratch. This suggests that what we need is a program which does the inference about what matters, and not to leave the job to a programmer. Such a program would require new algorithms in it, which is where the mathematician comes in. It would also have profound implications for our understanding of how brains work. Oh, and it would allow computers to see things, because it is dead easy to hook up a video-camera to a computer but rather hard to get it to tell what the camera is pointing at. This would mean huge gains in automation, and allow some fat businessmen to get very rich, which would be nice for them. I suppose.
The same kind of inference is involved in language learning. When a small child turns to its mother and says `Mummy, yesterday I seed two mans in the garden' it is demonstrating that it has extracted two rules from hearing speech samples: one is that putting `ed' on the end of a verb makes it past tense, and the other is that putting an `s' on the end of a noun makes it plural. This requires some rather clever distinctions to be made: the kid has extracted complex rules from data. The main complexity is working out when something is a noun and when it is a verb. This is not too far from working out when something is a little old lady and when it is a tree. Abstractly, the machinery is pretty much the same. Writing a computer program which could have an argument with you as a result of having acquired language in the same way you did, becomes a dim and distant prospect. Who knows, there could even be intelligent life on Earth eventually, even if it is made out of silicon.
This may not sound very much like mathematics to some of you, and it is true that there is not much classical, physics based calculus in it, but there is an interesting mix of statistical and geometric ideas.
If you are a mathematician or engineer with a Ph.D. or just feeling particularly brave, my Research Page gives a discussion of the motivation behind the work, and a sketch of some of the ideas. This might tell you if you want to go further. If you are already familiar with the field of Pattern Recognition, and in particular with the ideas of syntactic pattern recognition, go straight to my papers. Reading the papers should either quench your interest fast or stimulate it.
I took my honours algebraic topology students out to University House for lunch at the end of first semester 1996, and over food and Taylor's Cabernet Sauvignon ('91) challenged them to define an animal. This was for the purposes of formalising the idea of something which has sensors, effectors, and processes information in something like the way that nematodes, possums and people do. Since it seems unlikely that they will buckle down and do this, and since I was a bit off colour and unable to do more serious things, I decided to have a go at it myself. I haven't made up my mind whether the result to date is a demonstration of genius or of a mind unhinged by marking examination scripts. To form your own opinion, click here. This will get you a pdf file of about ninety pages which stops rather suddenly just as it starts to get interesting. It has grown a bit, particularly recently.
This is how a piece of mathematics can start out: it is a long, long way from being a serious mathematical model; it is concerned with trying to make precise some fuzzy ideas and this is an incremental process. With a lot of imagination you can see that it might one day be possible to do mathematical calculations, almost certainly on a humungous computer, which would allow us to say something about, say, political or economic matters. Just don't hold your breath.
Teaching
It is quite fun seeing the little bulb over somebody's head light up, although not as much fun as having my own little bulb light up. On the other hand, lighting up my own little bulb takes more hard work. Consequently, teaching students is a permanent temptation, and as I have given in to it all too often, it occupies much of my time and energy. Of course, it helps if they are bright. Gibbon said it better:
`The power of instruction is seldom efficacious except in those happy cases where it is almost superfluous'. Or words to that effect.
I used to have a teaching page with all sorts of interesting things on it, but it got out of date fairly quickly and some useless bastard moved some of the material so the links broke. Consequently I have scrapped it. If you want to know what I am teaching currently, go to the main UWA home page and chase links to find out what Mathematics there is and find me in there somewhere.
If you are already a student, or if just inquisitive, I have have produced over the years, for various courses, a few rather individual sets of notes which are in the form of essentially self-contained books. Students wishing to make up their minds whether to do some of the courses offered by the Mathematics Department (or contemplating selecting me as a supervisor and wishing to plumb the depths of my intellectual depravity) or foreigners from outside who wonder what exactly goes on at UWA in the undergraduate teaching, might wish to peruse some of these. I give the most recent as pdf files.
Warning: These books contain jokes. They may leave the humourless totally confused.
Introductory Mathematics
If desperate for light entertainment and there is nothing on TV, click
- here to get to the recent 2C2 book which gives a gentle and accessible introduction to differential forms.
- here to get a short course on Linear Algebra.
- here to get a simple treatment of Multivariate Calculus including Stoke's Theorem done in a relatively modern if scruffy manner.
Geometric Topology
If still desperate for light entertainment and there is still nothing worth watching on TV, the normal state of affairs, click
- here to get to some Notes I wrote to explain the background behind the text book for the course called The Shape of Space by Jeffrey Weeks. The book is quite delightful and I recommend it to just about anyone over the age of twelve.
- here to get my introductory treatment of Differential Geometry.
- here to get my latest opus on Geometric Algebra, which is what the Physicists call Clifford Algebras.
- The Road to Reality: A Review
- The Trouble With Physics: A Review
- Email:
Introduction to Differential Geometry
If interested in the way the universe works, click
Introduction to Geometric Algebra, or Clifford Algebras
If still interested in the way the universe works, click
Robotics
I wrote some informal notes on robotics for the third year course I gave for a number of years. They may amuse and entertain somebody; they amused and entertained me when I wrote them, and the students seemed to find them useful. Since they were intended for a mixed class of CS and Maths students, the standard is not very demanding. To get just under 200 pages of postscript on robotics, click on Robotics. The course is no longer given; it is perhaps better to pass lightly over the reasons for this.
Public Service Work
It
is thought that some of what an academic does might do the human race, society
or the Australian people a spot of good even if it can’t be called teaching or
research. This is the grab-bag,
the stuff we spend our time doing when we aren’t feeling clever enough to
understand the universe and there aren’t any students around to bore. Watching television doesn’t count, but
almost anything else does. I suppose even watching television might count in
the Arts departments, although one hopes not. One of my activities is writing
popular articles for Philosophy Now, a
popular magazine of ideas. Here they are in the form of PDF files as submitted.
And most recently Quantum Theory Lite, an introduction to the Mysteries with an explanation of the Bell Inequality and what it means:
-
I have also written a few articles for Quadrant, which being an Australian magazine for intellectuals does
not have many readers. Here are some of them, the articles not the readers:
I
live in the hope that they may persuade some people that Mathematics and Science are a lot more fun than they might have supposed from school lessons, and also rather important.
Administration
As every Australian Academic knows all too well, there are three things that we are supposed to do, Research, Administration and Teaching, of which the most rewarding financially is administration. We used to promote has-beens to do administrative chores and to increase their pay to compensate for the loss of prestige that goes with being a drudge. The laws of supply and demand have ensured that drudges now have the prestige, and the power to order things the way that drudges like them. My position on administrative chores is that I do what the Mathematics Department requires no matter how much valuable time it wastes on bizarre and pointless ritual designed only to placate meddling bureaucrats with an inadequate grasp of their own ineptitude. At the same time I point out the folly of it, vehemently. The only alternative is to join the bastards, which would leave me too full of self-disgust to function.
There are some honest administrators around who have come to it from honourable motives. I have met three, and there may be others. Two of them even have a sense of humour. They are usually very well organised but not very creative. Well, if everybody was like me the world would fall apart over the weekend, and an honest administrator who really works for the public good is a jewel to be treasured. We look at each other through the bars, each wondering which side is the zoo. I am prepared to admit that I need them, I can only hope they feel the same way about me. I doubt if those in Canberra do.
By contrast, what I think of the blinkered reptilian scum who get their jollies by working their way into politics in pursuit of status, prestige and the joys of pushing other people around, should not be put on a website which may be read by the young and innocent. To the blinkered reptilian scum I say: `Beware. Do not mess with me, or I will eat your eggs'.
Concluding Reflections for Taxpayers
If you are here to find out what University academics do to pass the time and have a deep suspicion that we are enjoying ourselves, then I have to tell you that much of the time we do. And this is why we work for lousy pay doing some heavy thinking that most people pay to avoid. And if you believe that some dim bureaucrat in Canberra can decide if what I am doing is worth what I am being paid, you are either innocent beyond decency or a dim bureaucrat in Canberra. In either case, it might be worth pointing out that when people love their work, and when they choose to do work you couldn't do because they are smarter than you, it is probably a good idea to let them get on with it. Meddling to see if they do it the way you want it done is probably a horrible mistake. It only slows them down and it wastes money spent on hiring meddlers.
So if you are a concerned taxpayer wishing to ensure that your money is being well spent, read, learn and by all means enrol at this University, and find out properly. Give us all the money you can afford and then leave us alone to spend it the way we want. Hardly any of us would spend it on fast cars or loose women, if only because the others would make sure we never got another bean. Mostly, what we want to do with it is beyond your comprehension. If it weren't, it WOULD be a waste of money.
This demand that you give us the cash and leave us alone may sound very odd, but historically, this has been found to be the best investment the human race has ever made. Hiring bureaucrats, by contrast, has been a good investment only if you want to stop progress dead in its tracks. Some people think this a good idea, but don't expect much sympathy from academics, particularly those in the technical areas.
You will find out by looking at other homepages that some academics are boring and some are irritating. I am one of the irritating ones.
So was Socrates.
But my real hero is Galileo, who got thrown out of the University of Padua for being rude about his colleagues. Most academics are rude about their colleagues, but only when they aren't there. This takes all the fun out of it.
Happy Netsurfing!
Contrary to any impressions you may have formed from reading the last few paragraphs, I am a cheerful little fellow and receptive to thoughtful comments, though usually somewhat busy. I am happy to receive questions or comments.
My address is...
and if that doesn't work try
- Snail mail:
Dr. Mike Alder,
Department of Mathematics and Statistics,
The University of Western Australia
Crawley WA 6009 Australia
- Phone: +61 9 380 3360
- Fax: +61 9 380 1101
mike alder, 15th May 2007