Wednesday, 8 January 2014

Mathematics as explained through Music

So in my head there are quite a few unnecessary connections, and the other day I realised that I think about music in a similar way to how I think about maths, and that lots of people do one or the other but the crossover is smaller than I'd like it to be.

So I'll start off with the obvious and move toward the less obvious - read less grounded connections.

Trigonometry. I think of trig (as the cool kids call it) like the piano, when you were younger someone else made you learn it and most people insist that they'll never use it again and move on with other things, but some people keep at it and it opens the door to all the other cooler mathsy/sciency things. It gets used all the time, in places you wouldn't expect it. I suppose this is where it falls apart a little because

Engineering Maths. I'm tempted to say this is like blues or jazz, really cool and requiring lots of skill to become famous but you'd know I'm lying. Engineering maths is more like the difference between a musical theorist and a composer, you have to know why this chord resolves into this one or what this instrument's tone is, but the composer takes all that stuff and then makes really cool stuff with it. No offense other mathematicians or music theoreticians. It just seems like this is where the people who like to have it all planned out gravitate towards.

Euclidean Geometry. Definitely the triangle. There was a time when saying things like "A line is a unique connection between two points" would have gotten you the gold star in maths, just like being able to reproduce a single note would get you a caveman Grammy. Those times are past and no one cares about plane geometry.

Non-Euclidean Geometry. The theremin. This is the maths to do with three dimensional space, which is much more bendy than you would think, and that of even more dimensions. So think of how a square is just a cube that you are looking at side on, non-euclidean geometry deals with shapes which are what you see when the cube isn't the end of the story, like if the cube is the three dimensional drawing of a higher dimensional shape. Then there's the whole Doctor Who opening theme.

Physics. I think of physics as the whole of musicology, because there's obviously maths in there, but there's also a stack of stuff you can't do with maths, or at least maths won't do with you because it isn't easy or nice. So it's like reading an Oliver Sacks book, long and oftentimes really cool, but you can only tell the funny anecdotes, no one wants to hear about all the science bits. Like the one about the entomologist whose perfect pitch was so accurate that he could tell the insect's wings vibrated at a C and were therefore buzzing at 32 Hz.

Calculus. The violin. Everyone knows it, and it's been the big papa in music for ages and ages. Fiddles and violins and other bowed instruments have been around longer than calculus by a long shot but both have dominated. When I think about music I confess the first instrument I think of is the violin, and all the famous melodies it's gotten. The same is true of calculus. When you do maths, there's a lot of calculus, you can't run away from it. It's the maths of change, and everything in the world is changing, all the time. You can do maths without calculus, but if you didn't have it at all the world would be a very very different place.

There are more kinds of maths and there are obviously more instruments and things, but those are the ones which are all tangled up inside my head.

Friday, 27 December 2013

I Miss the Family Business

"What do you want to be when you grow up?"

It's a question that you get asked consistently as a child, and more and more as you get older you're expected to have an answer. I think we could all be doing a better job of thinking about this question for more than the five seconds before we answer our relatives we haven't seen sine last Christmas. And to stop making the assumption that we know now that we are officially grown-ups.

I come from a reasonably large family so I've got the privilege of watching the process of people discovering what they want to do with their life or the approach they want to take with life at least. What I mean is I haven't really seen any of my siblings live a dream from the age of 8, investing their interest and spending their time on investigating every nuance of their future life. They did well at school, so they went to university and tried something out, sometimes it worked out, sometimes it didn't but they finished their degrees and they got jobs.

No one tells you what being in a particular job is like, or talks about why it is they travel across the world working for different companies. Or why they stay in the same job for fifty years. You're expected to glean what job you would enjoy based on your subjects at school, or something glamourised on TV. Maybe you will be able to do it, maybe the first thing you try is perfect for you and you never have to worry about your professional life and can just focus on other things. Maybe I sound a little disbelieving.

That's why I miss the family business, so that by default you have at least one thing you were involved in since day one, not as a fallback but as an introduction into the parts of life that many people don't see until they leave school, or university. I know a lot of business students who have never worked in a business, engineering students who have never been into an engineering firm and science students whose only experiments have been coursework. They haven't had to understand the point where you are convincing someone else to give you recompense for your services and your skills. If you ask people what they could do that people should pay them for I'm not sure you would get a good answer.

If this was the 18th century, my father would marry off some of his children, my older brother would inherit most of the stuff and continue in my father's work and I would go off to the church or become a man of science or something. But it isn't the 18th century, our lives have changed and we have a much broader array of options now. I don't think we have too many options, but I wonder if it's bewildering to be as free to choose as we are. Maybe doing the same thing our parents did would be good for us, because when you say "Sod this, I'm going to become the first person on the moon in fifty years" then you now have a plan.

I see a lot of people who go university because they did well at school, which they went to because at first it's government mandated and later because you go to school. They don't leave the education track for a long time, and then they find out that what they always wanted to do but never knew about, doesn't require anything they've learned. It seems strange to me to suggest that becoming educated is another rut that people can fall into but it happens.

I think this is why I wish we would bring back Take Your Kids To Work Day, because then maybe we could see how our parents, people we presume to know incredibly well, solved this problem for themselves, or how they are still working on it.

Our choices are delayed for us, parents work hard so we can try new experiences and not be pulled into the exact same lives as them. Maybe we should see what just what we are leaving behind before we walk out the door? Do we owe it to them and to ourselves to make as much use of these opportunities as possible?

Finally, I might disagree a little bit with what this guy says, I think most of you would be interested in seeing some alternatives to the education that I talked about last time. He's got goals and is self-directed which is something that is incredible to see based on our own preconceptions of how to treat 13 year olds and our assumptions of a teenagers ability to plan for their own future. So have a listen and see why I think we could all be doing a better job of thinking about what we want to be when we grow up.

Sunday, 1 December 2013

I hated school, and I bet you did too.

There are two very strange question that comes up from year 11 and 12's to people they knew from grades above. Maybe you played on their soccer team and walk past them at the shops, or you sang in choir with them, or you're dating their sister. Whatever the reason, when the opportunity comes up senior students will ask you "What's uni like?" and sometimes the follow up "Was it worth it?" There are some obviously implicit questions being asked here, beyond the simple curious or polite question about your new vocation as a coffee devouring university student.

And every time I've heard the question asked the answer from my mouth or anyone else is "Yes. God yes. You're going to love university." And this unequivocal answer is delivered without pause and pretty much without consideration for the person you're addressing because tertiary education, you feel, is indefinably better without having to worry about what degree the questioner wants to study or whether they are introverts or the life of the party.

These students want to know that all the things that they put up with at school are dealt with: that teacher they can't stand; uniforms; but most importantly, they attribute university as some kind of promised land, from brothers and sisters who have graduated before them to bring home stories about how much they enjoy it, older students who graduate before them, even a few teachers who relive their old glory days to students who want to know about where they're going next on what feels like rails.

And I hate it. Why shouldn't I? I detest the concept that the future should be better than the present, why not make what you're doing now worth telling people about rather than dreaming of going off to uni. I can only talk about the Queensland school system, but it has always felt like by the time I got to year 11 it was simply the last gate before the hallowed grounds of university. A final  hurdle to be jumped, not TWO WHOLE YEARS of time to learn things. The teachers would warn me that if I didn't work a bit harder I'd find to hard to get into my degree but the warning doesn't make sense. Shouldn't I be being warned that I was wasting their time and that these people know lots of cool things worth learning?

I don't want to spend the entire time talking about what I feel is an error in direction, in mindset for students, teachers, parents the whole high school ecosystem that has students sitting in the back of class biding their time to get out of school again. Students stuffed into uncomfortable uniforms sitting in uncomfortable chairs listening uncomfortably to teachers who are uncomfortable with the idea that 70% of these students would rather not have to listen and 10-15% have already taken up that idea. These children are present at school for 6-7 hours five days a week, it's two hours short of a full time job for them.

So what I'm urging is to have a look at when students come out of school, many go straight into university and they come back to school saying, by George university makes this school look like a nursery. Tutorials at university (which are the smallest class sizes) are the size of school classes, so we can rule out reducing class sizes to aid in learning (at least it isn't the most economical choice because smaller classes means more classes means more teachers and wages and classrooms and things).

What I think is needed is a change in the mindset I was harping on about before, I think students and teachers need to understand that they are there to learn things, to be educated, to have knowledge and curiosity shoved into their heads and be asked to go find out some things for themselves. Just like university, you aren't paying for and attending classes for the paper at the end, you're paying for the thing that happens in the middle, the learning bit.

That change in mindset would inform other changes in the school, professional sectors used metrics (evidence returned from clients about how they use products and whether a change in advertising or packaging or manufacturing increases sales and satisfacction) to inform their business approach for many years. Schools could do the same thing, if something isn't working then you change it, and if you don't know what isn't working but you can see there's a problem (yes, there's a problem if I laugh when people ask me what I liked most about school) then just change random things and see what happens.

Yes, I understand parents would object if you told them you're experimenting with their diddums but seriously would you rather tell them you don't care that no one likes school and everyone consigns 12 years of their memory to oblivion? Twelve years is a really really really really really really really really really really really long time, that was only 11 really's can you imagine what twelve years is like? (you didn't even read them all you just scanned them because of how bad it was) Rather than employing some more science and education graduates talk to some psych majors, I bet they have to read a hundred articles about learning methods for every one that the education guys read.

To get you, the people who make decisions at schools (I don't know if you're the ones with the titles and such or if you're the one standing behind that person) I have a crazy suggestion for you, I talked before about tutorials at university where students who are a year or two ahead who did well in that subject are asked to hold a class, and it seems to work because the students can get to know people one year older than them far easier than an adult who has twenty or fifty years on them. I've been on both sides of that scenario and I know that teaching a subject reinforces everything you know far better than when you take the subject.

So my proposition is this: take students, I don't care if they are your best student or the one who has just struggled through the year, take them to a class one or two years below and ask them to take the class. They'll know their stuff by the end of the lesson if they didn't before and the students may well pay more attention if the "teacher" is a grade 11 student. Because I have anecdotal evidence that students are passing grade 11 maths B without being able to add fractions properly. Which is something that is pretty well cemented in year 9 and you don't come back to it because as a teacher you don't have time to keep covering basic maths.

Let me be clear, this is not an attack on teachers or educators who have my utmost respect for spending time with children which is something I have spent my entire life avoiding. This is an attack on the institution of education which needs more of an update than the funding from the ever topical Gonski reforms. Thanks for reading and if you're in the position to change part of this, as a student, teacher, government worker, secretary, principal, head of school or parent then I'm urging you to give it a go and re-evaluate what you're asking for from the school and be understanding if the school looks like they are making a change.

Jumpy dance music to help you forget all about what I just said.

Sunday, 24 November 2013

Post Two "Gosh I'm Original" - Feat. Sunglasses

Due to Dr. Who Anniversary Special related internet blackouts I give it 24 hours before anyone actually sees this post.

I realised this week while window shopping that I had no idea how sunglasses are made, the sum total of my knowledge is that you grind the glass until it's i the right shape to focus light properly. I didn't know how the frames are made, how polarisation or tinting is made or how bifocal or multifocals mix their lens shapes.

So this is my summary, the polarisation film is made by spraying a layer of molecules which naturally align parallel to each other which cuts glare from light which is not aligned with the direction of these molecules. Usually glare is aligned horizontal to the ground, reflecting from objects like ocean waves and car windows slanted toward the cool shades wearing individual which is why the molecules are usually aligned vertically on sunglasses. The level of polarisation is affected by how misaligned the light is, so tilting your head may block more or less glare. The only reference to what kind of molecule was in a 1941 patent which described it as an "polyvinyl alcohol [solution] containing oriented molecules of polyvinylene" (Rogers, 1941) but I haven't found anything more recent, or anything suggesting optical manufacturers have updated their methodologies.

As for glass tinting all I could find was that most optical glass is made by immersing the glass in a chemical bath and the tint soaks in to a much greater depth (150 microns) than the thickness of a sprayed coating as was initially tested (5 microns thick).The only chemical I could find which was used for tinting was a combination of layers of titantium oxide and nickel hydroxide, although I couldn't find if these chemicals were in widespread use in this application.

The frames themselves were made by a couple of different processes, differing on the material and style. Wire frames are bent into shape with a collection of different machines which twist through certain angles to make different shape lens frames and bridges which are brazed together. Plastic is injection moulded with a die (metal pieces which act like moulds) which is cut to produce a specific style.

Multifocals and progressive lenses (lenses whose power varies around the lens) are made by using a standard front side of the lens and then the back is ground to different shapes for each patient.

Word of the day/week/whatever: hypoallergenic, as in doesn't cause allergic reactions.

Live fast and die old, please. Or never, you know. Depending on how legitimate these claims are. TED talks are crazy.

1941 Patent: http://www.google.com/patents/US2263249
Berkeley article on new tinting options (new for 1998): http://www.lbl.gov/Science-Articles/Archive/cheap-photochromics.html

Sunday, 17 November 2013

Page One

    As the title suggests, this is the opening page of this blog and it should act as a guide to what will follow in the improbably infinite number of continued ramblings. The books in the background are  not to suggest I am the owner of some mighty tome of knowledge but because I believe that the written word is humankind's greatest invention and books still carry that connotation. Think of this post as the front page of my newspaper. So obviously what will follow is the editorial, wherein I will try not to drive you away. 

    Dear New Reader,

    Hopefully this is the beginning of a long relationship of me talking nonsense into the internet and you consuming it in your underwater palace/fortress of solitude/hermetically sealed chamber.

    So to initiate proceedings I'm going to talk about myself for approximately one more paragraph and then I'll avoid doing it ever again. I want this blog to achieve a couple of goals. (I hope listing them will help me focus in on them as much as it helps you to close this tab if you don't want to read them, which I hope is different from disliking said goals) The idea is all my opinions, grievances, advice, questions, and actions will all be motivated by a desire to disseminate knowledge. I don't mean science or to act as a library, I want to make/help/push you into a different viewpoint by talking at you a couple of times a week about things that I like/hate/encourage/disagree with/think should be explored more/argue should be boycotted or ignored/argue shouldn't be ignored/want to remind you about because it's been a while and just like that person who's name you forget but really really should remember this is thing to store in that fabulous brain box of yours.

    In essence I want this to be my own news clippings, scrapbook, and collage which you get to share in because you like to flip through other people's things when you're at their house too.

    I'm not going to say anything about making it this far because you either did or you didn't. Instead I'm going to kindly gesticulate madly towards page two and the deluge of opinions.

    PS, I really want to this to feel informed and unbiased. So if you feel like I start to favour some side of a discussion or discriminate I definitely want to hear about it.

*****

    I thought about starting off with something light and fun about being a college student but I decided that can wait for when I'm out of ideas (i.e. if I title a post "10 Reasons Why College is the Best" what it really means is it'll be my final post) so I discarded that and decided it'll be something that I've been thinking about all week.

    To be a incremental fraction more specific: Staring. To focus our collective perspectives what I mean is the kind of staring where you catch someone in the corner of your eye and you think, my - insert particular reason for this existence here - what a stunning artwork has been moulded through cellular growth, life, and decay. Why if that isn't something I could drink in for eternity, I should wax lyrical upon this subject. That kind of staring. Because it isn't really staring, it's objectification. (I'm sure you all think along those lines when you do it, I know we've all got a little adoring lyricist in our mind who composes soliloquies when given the perfect stimulus) This is the word we use when we see/smell/detect in some meaningful way someone else and render them down to constituent parts and select those we like and take the bits we like to admire. Thereby rejecting the resulting pile of liver, back hair, and soles of their feet (things I suspect are rarely objectified). 

    I want to put forth my own opinion first because I'm selfless like that. I've tried to render it down as simply as possible when I say that I think actions can be understandable without being forgivable or more importantly acceptable. What we do is always under the scrutiny of our company, which I should remind you includes yourself. And now that you've read this it includes me.

Intuitively we know that some of our actions can appear creepy, or that things we do should seem odd/antisocial (the actual meaning of disrupting society in some way) but we can get away with them because we're attractive or fun or some other balancing factor is in play like a one sided power relationship. So today I want to remind you of that; to check one of our standard behaviours can really change how people see you to better match how you see yourself.

    So to make a final suggestion to reinforce things we already know about ourselves, we don't want to be genderist because we are developed people who are capable of exercising our own self control.

    To finish up, each post I'm going to try to make my sign off a link to something I've found, which while knowing nothing about you dear new reader I can accurately predict you will enjoy or find insightful. This week it's a song which has been in my head all week. Now it can be in yours too.