I like helping people with their homework on the internet. I do this when I can on physicsforums.com, which is a forum for discussing physics, and philosophyforums.com, which is for discussing philosophy. Both have sections where people can ask questions about problems they are having trouble understanding – usually for homework in a degree course. The physics forum has Help sections covering physics, mathematics and chemistry. The philosophy forum’s Help section is focused on symbolic logic, which is a branch of maths closely related to set theory.
There’s an art to both asking and answering questions on such forums. It is not acceptable to just post a question straight out of an assignment and hope somebody solves it for you. That would be lazy, and possibly also cheating. Equally, it is not the done thing to just post a solution to somebody’s problem, even though that would often be the easiest thing to do. The paradigm of quality advice on the internet seems to be to give carefully chosen hints that will lead the student towards being able to solve the problem by themself. It is quite challenging to choose one’s hints to be not so obvious that they give the game away, and not so obscure that the student remains helplessly lost.
Now you might expect there to be an imbalance between people needing advice and people offering it, so that many people remain unhelped. Well there is an imbalance, but it’s the other way around. There are far more willing advisers than there are people wanting to be advised! How does such an odd situation arise? I can only guess at it based on my own attitude to internet advice – which is that I love giving it. I think there is a deep-seated need in most humans to feel useful. In some it is stronger than others, and in me it is quite strong. In some professions, like being a doctor, one has frequent opportunities to provide advice to one’s acquaintances. People seem to have an inexhaustible appetite for free medical advice. But the knowledge of art critics, journalists, electricians and accountants is drawn upon far less frequently in private life. Of course people would be very happy to draw upon the skills of an electrician without cost, for instance to get them to fix some circuits in one’s house. But that is very different from asking for advice. Spending an hour alone in a dusty roof cavity fiddling with dangerous wires is far less fun than dispensing advice to an agog and appreciative audience. A notable example of this difference is the poor old professional photographer. Goodness knows how many times they get asked by friends, relatives and acquaintances to come to a wedding and take some photos – for no fee, of course. And like the electrician in the attic, it is solitary work, with little appreciation except at the time when one actually delivers the photos.
The few professional photographers I have known have had policies of not doing photography for anybody’s wedding except as a fully professional, paid gig. I thought that policy a bit harsh when I first came across it. But after reflection I realised it was the only way to end up avoiding spending countless hours doing work for free, as well as missing out on being able to enjoy one’s friends’ weddings. Life is hard enough for photographers these days, with news organisations slashing their headcounts of journalists and photographers – preferring to just get stock clips from Getty images. It adds to the woe to be be constantly asked to work for nothing.
On the other hand, if people were to gather around them in adoring circles at parties, asking their advice on shutter speeds, apertures, lenses and filters, that would be a different thing altogether. So far as I can tell, that doesn’t happen very often.
My areas of expertise are not under such hard times as photographers, but neither are they as socially sought-after as those of doctors. They include finance, music, bicycles and fitness, philosophy, physics and mathematics. Once or twice a year I get asked for advice on bicycles, fitness or investment. I don’t think I’ve ever been asked about physics, philosophy, music or maths, unless we count my children asking for homework help when they were little.
So, to fulfil my need to feel useful, I go to the internet to see who needs help integrating x sin x, working out whether a pendulum has enough energy to swing right over the top of its arc, working out whether ‘Dark Energy’ would break a wire stretched between two galaxies, or understanding the significance of the Bell Inequality or Godel’s First Incompleteness Theorem.
And what do I find when I go there? Any question that is expressed even moderately clearly has received three or more responses within half an hour of being posted. It’s almost as though people are falling over one another to be the first to respond. You might think that one response is all that’s needed. But it’s not. There is often room to contribute even when there have already been two or three responses to the request. Remember that answers are supposed to be hints, not answers to the homework problem. The best answers are often in the form of questions to the original poster, like ‘what is the component of the gravitational force that points diagonally down the banked track?‘ They serve just to get the student thinking in the right direction, or even in just a more productive manner. Often responders need to ask questions to clarify the problem because the student has not explained it well enough. In logic, the standard question is ‘what tools are you allowed to use?‘ because the typical problem is to prove a statement, given a number of premises and a set of deduction rules, and there are many different logical systems, with different ‘toolboxes’ of deduction rules. Most students just post ‘how do I prove such-and-such, given the following premises’, without specifying what tools are available to them.
So I still sometimes find questions to which I can helpfully respond. Some questions are expressed so unclearly that nobody wants to touch them. I quite enjoy the forensic work of trying to work out what the communicationally-challenged student was trying to say. In other cases, the question may be clear enough but the responders may have gone off on a false trail, or been insufficiently clear, leaving room for me to contribute. But it’s only the occasional question that I find has received little enough helpful attention for me to respond without giving too much of the answer away.
I have said that I get enjoyment from answering questions. And maybe I am a little more than averagely susceptible to enjoying the fulfilment that comes from that. But there are many people that seem to have a much stronger desire for that fulfilment than I. Many of the responders have made tens of thousands of posts to the forums, and their presence can be seen in most of the questions ever asked. Those that have responded to very large numbers of questions have little electronic trophy icons below their on-line avatar, saying things like ‘Homework Helper’. It reminds me of the Fat Controller, who would occasionally, when Thomas or one of his friends had done especially well, reward them by proclaiming that they were a Really Useful Engine – the ultimate accolade!
Why do people like helping so much on the internet? This wish to be useful is so widespread, and so strong. And it isn’t mirrored in off-line life – or is it? Perhaps it is. Most doctors appear to enjoy being consulted by family and friends on the selection of a surgeon for Tristram’s grommets, and I’m sure the electrician would revel in the opportunity to dispense wisdom on the difference between the connections of a Neutral and an Earth wire, as long as they weren’t then dispatched to the attic to do some free clipping and splicing. I once consulted an electrician on just this topic and, as far as I could tell, they enjoyed providing the information.
Is it possible to harness this human tendency? There are so many people in the world that need help and don’t get it. Maybe it is. But on the other hand maybe the seeming disconnect between the large number of willing advisers on the internet and the large number of people in real life desperately needing help can be explained by the above-mentioned difference between advice and work. Giving advice is often easy, takes little time, costs nothing and is a social activity, as one does it in conversation with the advisee. Work, on the other hand, whether it be fixing wires, taking photos, preparing a pathology slide, or constructing a Monte Carlo model to measure financial risk is time-consuming, usually solitary and often frustrating.
There are exceptions. I’ve always liked the idea of raising a barn, like the Amish do in Pennsylvania, because it seems such an enjoyable, social, neighbourly form of work. Sadly, not many barn raisings happen in my neighbourhood.
Bondi Junction, August 2015
Do we all have things we look forward to learning? In early 1983 I was very excited about learning the meaning of ‘Direct decomposition of a finitely generated module over a principal ideal domain’. That was the name of the central section of the main text for my second year uni algebra course. The text was ‘Rings, Modules and Linear Algebra’ by Hartley and Hawkes.
I understood from the course summary and the blurb on the textbook that learning how to do the activity described by the above italicised phrase was one of the main goals of this course.
What I found particularly appealing about the goal was that it referred to three different things, none of which I knew what they were. What is direct decomposition? Dunno! What is a finitely generated module? Dunno! What is a principal ideal domain? Dunno!
To add to the titillating obscurity of the subject, each of the three things was qualified by an adjective or adverb. The first two things only had one qualification each: direct decomposition rather than just any old ordinary decomposition, and finitely-generated module rather than just a commonorgarden module. But the third thing actually had two qualifications. This was not just an ideal domain or a principal domain but it was a principal, ideal domain. How exciting is that?
(Mathematicians may wish to object that the comma does not belong, and that the word ‘principal’ actually qualifies the word ‘ideal’ rather than the word ‘domain’, so that ‘a principal ideal is a thing’, whereas a ‘principal domain’ and an ‘ideal domain’ are ‘not a thing’, to borrow the ‘thing’ terminology that seems to be so popular amongst today’s young people. But let’s not allow this minor technical point to spoil a good story).
Why, you might wonder, was I so fascinated by a topic with so much jargon in it? What, you might ask, and perhaps not entirely without reason, is my problem?
The answer, I think, is that I have a fascination with jargon, and more generally with weird, obscure and bizarre things. The jargon has to be justified though. I have no interest in the jargon invented by some professions (merchant bankers and stock brokers in particular come to mind) to describe perfectly ordinary concepts in obscure ways in order to make them appear clever to others and justify their exorbitant fees. No, what excites me is jargon that people have no choice but to invent because the concepts it is describing are so abstract and complex that ordinary words are useless.
The jargon of mathematics and many of the sciences is of this justified type. When a physicist tells you that the steps necessary for predicting the perihelion of Mercury include performing a contraction of the Riemann tensor and another contraction of the Ricci tensor in a Swarzschild spacetime, or that the possible states of a carbon atom form an exterior algebra generated by the Hilbert spaces of electrons, neutrons and protons, she is describing things that cannot be described in plain language. And yet they are real things, not just insubstantial ideas. They are things that enable humans to perform wonders.
More to the point though, when Doctor Who announces that he has ‘Reversed the polarity of the neutron flow’, we learn that as a consequence of this linguistic peculiarity the universe, which was about to have its space time continuum rent asunder (ouch!), has been saved. This is no postmodernist proliferating syllables for the sake of mystery and pomposity, as in:
“We can clearly see that there is no bi-univocal correspondence between linear signifying links or archi-writing, depending on the author, and this multireferential, multi-dimensional machinic catalysis.” [Felix Guattari]
At heart, I think my fascination with genuine jargon is just part of an insatiable curiosity. The world is so full of intricate patterns and amazing phenomena, yet we will only ever get to see a tiny part of what is there. I want to find out what I can while I have the chance.
I can’t remember much about that 1983 algebra course, but I can picture that topic title going around and around in my brain like an obsession. I particularly remember running around the uni oval in athletics training, thinking as I went that within a few months I would actually be one of the privileged few that understood ‘Direct decomposition of a finitely generated module over a principal ideal domain’, even though at that time I had no idea of what it even meant. It was like counting down the days to Christmas.
I can’t remember the point at which we finally learned how to do it. Perhaps it was a bit of an anti-climax. Perhaps it turned out not to be as exotic as it sounded, or familiarity had bred contempt (or at least dissipated some of the awe) by the time we neared the end of semester.
As well as spoken jargon I also have a taste for unusual symbols. In primary school, when everything we do in maths is a number, the idea of doing algebra in high school, where we would use letters rather than numbers, seemed very grown-up. In junior high school we could look forward to trigonometry with those funny sin, cos and tan words, then logarithms and exponentials with log x and superscripts ex and then, even more alluring, calculus in senior high school with those loopy integral signs ∫.
At uni I couldn’t wait to be able to use the ‘plus’ and ‘times’ signs with circles around them – ⊕ and ⊗, the special curly ‘d’s that are used for partial differentials ∂. And the upside-down triangle ∇. I imagined it would be like learning a secret language, into which only specially selected people would be initiated (Yes I was vain! So sue me. What privileged, talented 20-year old isn’t?) As it turned out I didn’t get to use ∂ much, and didn’t get to learn about ⊗ or ∇ at all, because of my subject choices.
I very much wanted to learn about ‘tensors’. I had heard that they were like matrices (rectangular tables of numbers that all maths students have to study in first year uni) only more complex, and that you needed them to do relativity theory. But again I missed out because of my subject choices. Not that I regret that. If I hadn’t made the choices I did, I’d have missed out on learning about finite-state automata and NP-complete problems, and would never have had the opportunity to design a computer chip that converted binary to decimal or to write parallel-processing computer programs to simulate populations of aliens (that’s beings from other planets, not the human immigrants the Tea Party are so worried about).
Over the last few years I have rectified my lamentable ignorance of tensors, ⊗ and ∇, as a consequence of my mid-life crisis. Some people buy red sports cars and get plastic surgery. I decided I couldn’t live another year without understanding General Relativity and Quantum Mechanics. It takes all sorts, I suppose.
An unexpected bonus of this flurry of crisis-induced self-study was two new hieroglyphics 〈x| and |y〉 – complete with funny names: ‘bra’ and ‘ket’ (because when you put them together to make an ‘inner product’, written 〈x|y〉, you make a ‘bra[c]ket’ – get it?).
An unexpected bonus of this flurry of crisis-induced self-study was two new hieroglyphics 〈x| and |y〉 – complete with funny names: ‘bra’ and ‘ket’ (because when you put them together to make an ‘inner product’, written 〈x|y〉, you make a ‘bra[c]ket’ – get it?). That affords me the smug satisfaction of being able to understand – if not necessarily able to follow – most of what is written on the sitting-room white board that’s often in the background in The Big Bang Theory. And yes, it usually is real physics or maths, not just made-up jumbles of unrelated symbols. Sometimes it’s even relevant to the story-line, like when Sheldon had Permutations and Combinations of a set of 52 elements written on the board, because he was trying to figure out a magic card trick one of the others had done (not that they ever referred to the board). That’s in contrast to Doctor Who, where they just sling any old combination of fancy words together (‘Reverse the polarity of the neutron flow’ is not a ‘thing’. Or at least, it’s not a ‘thing’ you can do.).
I’m not expecting this essay to resonate with many people. It is a rare perversion to be intrigued by arcane language and symbols. But perhaps it’s not unusual for people to long to learn something or other that is currently far beyond their knowledge or abilities. It might be how to crochet an intricate doily, to speak a foreign language fluently, to recite The Rime of the Ancient Mariner from memory or, when a bit younger, yearning to be able to ride a bicycle without training wheels, swim the Australian Crawl or play a piano with both hands at the same time.
Bondi Junction, March 2014