Doctor Sophie Explains the Joy of Maths
Jun. 3rd, 2012 07:24 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
alias_sqbrI did a meme on Tumblr where I would do a audio/voice post on any topic I was given. And kentsarrow gave me the topic maths! If you don't like maths you can ignore me and watch my cat wondering that on earth is going on :D
I edited and recut it a bit to remove errors and repetition, something that ended up getting lost is the fact that if you stick with maths when you think you're bad, and get competent help with the aspects you're struggling with, you should be able to achieve a lot of improvement, and maybe even find you're not "bad at maths" after all. Skills are more learned than innate (something I need to remind myself of more often, I would say, based on this stream of consciousness rant)
Transcript:
Hi! This is Sophie. I'm just going to shift my face so it's under the recorder.
So. I did this meme saying I'd talk or record a video about any topic I was given, and I was given the topic of maths by kentsarrow. And on the one hand is a topic I have a lot of opinions about but on the other hand its such a huge topic, I was like "Oh God what do I say?" So I'm just going to say whatever pops into my head.
So what to say about maths? For a start: maths is great. It's much cooler than people think. I really enjoyed it... that's my cat, Kira, she doesn't like maths so much.
"A Phd in maths, that must mean adding numbers all the time, right?"
Well A, no, that wasn't what I was doing, and B I'm actually not all that good at addition, subtraction or multiplication, I used to be good at them back when I was a kid...unless it involved time. You give the difference between 2:30 in the afternoon on a Tuesday and 4:30 in the morning on a Wednesday and I have no idea, time zones baffle me...but other kinds of addition I used to be good at and then I got older and it all got smooshed out. So what did it get smooshed out by?
For me: algebra. I absolutely adore algebra, the idea of getting beyond concrete numbers or objects and dealing with an abstract idea of an object or a number or a quantity. And my favourite kind of algebra is abstract algebra. Group theory, what I ended up doing my Phd in, that's when you come up with these theories and facts that are true about a whole range of objects and things, and you can just plug them into your proofs.
So if you have something and it's true for say...binary numbers, zero and one. So it goes zero, zero plus one is one, one plus one is zero, zero plus one is one and so on and so forth. That's the binary numbers, and then there's zero, one, two, and so on, and that's...I'm not sure what that's called, but base three. And then you've got rotations, so you've got an object, let's use...this remote control, and arbitrary object. And so zero is going to be leaving the object alone, and one is turning it over. So zero plus zero is zero. Zero plus one is one. One plus one...is zero! And so rotation by 180 degrees is mathematically equivalent to the numbers zero and one in binary.
I thought I was done, this is an extra section I'm going to add in the middle because I got the maths wrong. I guess that just goes to show that getting numbers right and having a mathematical brain are not necessarily the same thing. Here is the example of rotations equivalent to zero, one, and two in base three.
So here we have an arbitrary object (another remote) which you'll notice is different to the previous arbitrary object, and it's still mathematically equivalent, I could even use my water bottle but this is smaller.
We're going to define three rotations: this is zero degrees, which is zero, this is 120 degrees which is one, and this is....240 degrees which is two. You'll notice that if you add 120 to 240 you get 360, which is zero. And so our rules are: zero plus zero is zero. Zero plus one is one. One plus one is two. Two plus one is zero. And so two plus two is one. And if you count on your fingers you go zero, one, two, plus one is zero, plus one again is one. So two plus two equals one in base three. So the maths of rotations by 120 or 240 degrees is the same as the maths of zero, one, and two in base three.
Now I have those numbers right, before I was saying it was 60 degrees which is a totally different angle. Hooray for me not being very good at geometry.
...and you can take that to higher levels, so you can deal with a whole bunch of different stuff without having to deal with the actual stuff. So if you're someone like me who forgets what number a rotation by a third of a circle is but you understand the idea of doing something three times and ending where you start, then this kind of mathematics really appeals. It kind of feels like you're understanding the basic structure of the universe. I used to study theoretical physics, I wanted to be a theoretical physicist, I wanted to be like Stephen Hawking except not in a wheelchair HA HA THAT TURNED OUT WELL, I got the wrong side of that bargain, I'm in a wheelchair but don't know much about theoretical physics.
Anyway, it turned out that theoretical physics for me was too real world. There was too much emphasis on solving mucky equations with rough terms where you...what's the word, it's a disgusting word, they do it in engineering...they don't do it in pure mathematics so I never do it...estimate! Estimating things makes my skin burn. There was this point in physics in second year where they said "The equation sin (wobbly line) looks a lot like the equation x (straight line going up at 45 degrees) around zero, because x goes like this, and then goes like that, while sin goes like this, and then goes like that. So everywhere we see a sin, which is a complicated function, we'll just replace it by an x." And I thought "But you haven't said when. You're just going to replace all the sins. So sin infinity...ok, sin a million is about one or zero, while a million is a million. So you're saying a million is roughly equal to one? Sometimes? No! That makes no sense! Why are you doing this? It's not right! I want exact values! I want perfection! I want the spheres of the universe in this constant beautiful pattern!" So I quit physics and went into pure mathematics and never learned anything useful again.
Well, that's not true. My thesis is used by other mathematicians, and those mathematicians make theories which are used by more practical mathematicians, which are then used by physicists which are then used by engineers which are then used by actual people in the real world doing useful stuff. So, you know, maybe in a hundred years or so the stuff that I discovered will be useful to someone in a practical sense, but it makes me happy.
This is also why I went into teaching. I wanted to share the theory with everyone. And then I discovered that other people weren't as excited about maths as I was. When I tried to get the six year olds to get excited about the four colour theorem, it didn't turn out so well, and I quit that job too. Ahem! This isn't about my career as a mathematician and how it didn't turn out very well, this is about how maths is great!
Maths is a lot of fun. I'm not one of these evangelical people who thinks that everyone should love maths, if you don't love it that's fine, I don't love geography. I tried, maps just baffle me, I don't understand them. I have friends who love geography, that's good for them, I can understand that they don't hate it the way I do, it obviously makes them happy and that's fine. It's like we're in different fandoms, I'm not going to geography shame them.
Ok, I'm going to add a little bit more at the end because I descended into incoherence before. What I want to say, that I don't think I really got across before...let's see if I can say it now...
Basically, I don't like the fact that it's assumed that either you're good at maths, in which case you're probably using it to make lots of money (haha not necessarily) and are really really smart at everything and generally smart and then you can enjoy it OR you're stupid, and you should hate yourself and hate the subject and force yourself to learn it because you need it to make money but it's not actually fun. And I think that's ridiculous. I think maths is a tool, I think there's different kinds of thinking, different kinds of training, that make you better or worse at different kinds of mathematics- and there isn't just one kind of mathematical thinking, there's certain kinds of maths I'm just not all that good at, certainly by comparison. I know people who are amazing at adding things up in their head. My mum failed highschool maths, or didn't do very well in highschool maths, but she can add up like a whiz, and she really enjoys that, and I think that's fine, I don't think she should go "Oh, I'm terrible at maths, I shouldn't enjoy it at all" I think people should be encouraged to enjoy...the same way that people should be encouraged to enjoy sport, even if they suck at it. I suck at sport, and now obviously I suck at, you know, walking. But when I was younger I wish that I'd been taught to enjoy the sheer physicality of playing games and stuff even if I was terrible.
And I think that even if you're not as good as the average, if you're not as good as you'd like to be at maths, you should still be able to enjoy the stuff you do without feeling self conscious about not knowing everything, about not being "good enough". There's no "good enough".
One of the things I learned during my Phd...I'd always been smarter than everyone most of my life, or at least near the top, and all these people were smarter than me, I was nothing, because that's what a Phd is all about, destroying your self esteem. And it took me a while to realise it didn't matter. I mean, I'm not the world's best artist but I still draw and I enjoy it, and I think maths should be like that: it's a tool, and it's fun, and if you enjoy doing puzzles or whatever good for you, and it shouldn't be...we should be taught to enjoy it and to use it when we need it, and if you need a bit of help there's no shame in that, we all need help sometimes, and you shouldn't be made to feel like a bad person. That's basically my ex maths tutor rant. I wish we could all enjoy maths, to the extent that we need it and want to do it.
So: YAY MATHS. That's my moral.
I edited and recut it a bit to remove errors and repetition, something that ended up getting lost is the fact that if you stick with maths when you think you're bad, and get competent help with the aspects you're struggling with, you should be able to achieve a lot of improvement, and maybe even find you're not "bad at maths" after all. Skills are more learned than innate (something I need to remind myself of more often, I would say, based on this stream of consciousness rant)
Transcript:
Hi! This is Sophie. I'm just going to shift my face so it's under the recorder.
So. I did this meme saying I'd talk or record a video about any topic I was given, and I was given the topic of maths by kentsarrow. And on the one hand is a topic I have a lot of opinions about but on the other hand its such a huge topic, I was like "Oh God what do I say?" So I'm just going to say whatever pops into my head.
So what to say about maths? For a start: maths is great. It's much cooler than people think. I really enjoyed it... that's my cat, Kira, she doesn't like maths so much.
"A Phd in maths, that must mean adding numbers all the time, right?"
Well A, no, that wasn't what I was doing, and B I'm actually not all that good at addition, subtraction or multiplication, I used to be good at them back when I was a kid...unless it involved time. You give the difference between 2:30 in the afternoon on a Tuesday and 4:30 in the morning on a Wednesday and I have no idea, time zones baffle me...but other kinds of addition I used to be good at and then I got older and it all got smooshed out. So what did it get smooshed out by?
For me: algebra. I absolutely adore algebra, the idea of getting beyond concrete numbers or objects and dealing with an abstract idea of an object or a number or a quantity. And my favourite kind of algebra is abstract algebra. Group theory, what I ended up doing my Phd in, that's when you come up with these theories and facts that are true about a whole range of objects and things, and you can just plug them into your proofs.
So if you have something and it's true for say...binary numbers, zero and one. So it goes zero, zero plus one is one, one plus one is zero, zero plus one is one and so on and so forth. That's the binary numbers, and then there's zero, one, two, and so on, and that's...I'm not sure what that's called, but base three. And then you've got rotations, so you've got an object, let's use...this remote control, and arbitrary object. And so zero is going to be leaving the object alone, and one is turning it over. So zero plus zero is zero. Zero plus one is one. One plus one...is zero! And so rotation by 180 degrees is mathematically equivalent to the numbers zero and one in binary.
I thought I was done, this is an extra section I'm going to add in the middle because I got the maths wrong. I guess that just goes to show that getting numbers right and having a mathematical brain are not necessarily the same thing. Here is the example of rotations equivalent to zero, one, and two in base three.
So here we have an arbitrary object (another remote) which you'll notice is different to the previous arbitrary object, and it's still mathematically equivalent, I could even use my water bottle but this is smaller.
We're going to define three rotations: this is zero degrees, which is zero, this is 120 degrees which is one, and this is....240 degrees which is two. You'll notice that if you add 120 to 240 you get 360, which is zero. And so our rules are: zero plus zero is zero. Zero plus one is one. One plus one is two. Two plus one is zero. And so two plus two is one. And if you count on your fingers you go zero, one, two, plus one is zero, plus one again is one. So two plus two equals one in base three. So the maths of rotations by 120 or 240 degrees is the same as the maths of zero, one, and two in base three.
Now I have those numbers right, before I was saying it was 60 degrees which is a totally different angle. Hooray for me not being very good at geometry.
...and you can take that to higher levels, so you can deal with a whole bunch of different stuff without having to deal with the actual stuff. So if you're someone like me who forgets what number a rotation by a third of a circle is but you understand the idea of doing something three times and ending where you start, then this kind of mathematics really appeals. It kind of feels like you're understanding the basic structure of the universe. I used to study theoretical physics, I wanted to be a theoretical physicist, I wanted to be like Stephen Hawking except not in a wheelchair HA HA THAT TURNED OUT WELL, I got the wrong side of that bargain, I'm in a wheelchair but don't know much about theoretical physics.
Anyway, it turned out that theoretical physics for me was too real world. There was too much emphasis on solving mucky equations with rough terms where you...what's the word, it's a disgusting word, they do it in engineering...they don't do it in pure mathematics so I never do it...estimate! Estimating things makes my skin burn. There was this point in physics in second year where they said "The equation sin (wobbly line) looks a lot like the equation x (straight line going up at 45 degrees) around zero, because x goes like this, and then goes like that, while sin goes like this, and then goes like that. So everywhere we see a sin, which is a complicated function, we'll just replace it by an x." And I thought "But you haven't said when. You're just going to replace all the sins. So sin infinity...ok, sin a million is about one or zero, while a million is a million. So you're saying a million is roughly equal to one? Sometimes? No! That makes no sense! Why are you doing this? It's not right! I want exact values! I want perfection! I want the spheres of the universe in this constant beautiful pattern!" So I quit physics and went into pure mathematics and never learned anything useful again.
Well, that's not true. My thesis is used by other mathematicians, and those mathematicians make theories which are used by more practical mathematicians, which are then used by physicists which are then used by engineers which are then used by actual people in the real world doing useful stuff. So, you know, maybe in a hundred years or so the stuff that I discovered will be useful to someone in a practical sense, but it makes me happy.
This is also why I went into teaching. I wanted to share the theory with everyone. And then I discovered that other people weren't as excited about maths as I was. When I tried to get the six year olds to get excited about the four colour theorem, it didn't turn out so well, and I quit that job too. Ahem! This isn't about my career as a mathematician and how it didn't turn out very well, this is about how maths is great!
Maths is a lot of fun. I'm not one of these evangelical people who thinks that everyone should love maths, if you don't love it that's fine, I don't love geography. I tried, maps just baffle me, I don't understand them. I have friends who love geography, that's good for them, I can understand that they don't hate it the way I do, it obviously makes them happy and that's fine. It's like we're in different fandoms, I'm not going to geography shame them.
Ok, I'm going to add a little bit more at the end because I descended into incoherence before. What I want to say, that I don't think I really got across before...let's see if I can say it now...
Basically, I don't like the fact that it's assumed that either you're good at maths, in which case you're probably using it to make lots of money (haha not necessarily) and are really really smart at everything and generally smart and then you can enjoy it OR you're stupid, and you should hate yourself and hate the subject and force yourself to learn it because you need it to make money but it's not actually fun. And I think that's ridiculous. I think maths is a tool, I think there's different kinds of thinking, different kinds of training, that make you better or worse at different kinds of mathematics- and there isn't just one kind of mathematical thinking, there's certain kinds of maths I'm just not all that good at, certainly by comparison. I know people who are amazing at adding things up in their head. My mum failed highschool maths, or didn't do very well in highschool maths, but she can add up like a whiz, and she really enjoys that, and I think that's fine, I don't think she should go "Oh, I'm terrible at maths, I shouldn't enjoy it at all" I think people should be encouraged to enjoy...the same way that people should be encouraged to enjoy sport, even if they suck at it. I suck at sport, and now obviously I suck at, you know, walking. But when I was younger I wish that I'd been taught to enjoy the sheer physicality of playing games and stuff even if I was terrible.
And I think that even if you're not as good as the average, if you're not as good as you'd like to be at maths, you should still be able to enjoy the stuff you do without feeling self conscious about not knowing everything, about not being "good enough". There's no "good enough".
One of the things I learned during my Phd...I'd always been smarter than everyone most of my life, or at least near the top, and all these people were smarter than me, I was nothing, because that's what a Phd is all about, destroying your self esteem. And it took me a while to realise it didn't matter. I mean, I'm not the world's best artist but I still draw and I enjoy it, and I think maths should be like that: it's a tool, and it's fun, and if you enjoy doing puzzles or whatever good for you, and it shouldn't be...we should be taught to enjoy it and to use it when we need it, and if you need a bit of help there's no shame in that, we all need help sometimes, and you shouldn't be made to feel like a bad person. That's basically my ex maths tutor rant. I wish we could all enjoy maths, to the extent that we need it and want to do it.
So: YAY MATHS. That's my moral.
