How the universe got its spots …
… is the name of a book I’m reading, written by Janna Levin and subtitled “Diary of a finite time in a finite space”. The book is written as a series of (unsent) letters addressed to her mother which, as the jacket cover says, relate “her own personal and intellectual journey through space and time”, while covering such topics as relativity, quantum mechanics, black holes and the big bang.
Until I reached the sections which start talking about topology, I was doing quite well and mostly understanding things. I did understand the difference between geometry and topology, “geometry is about curves and smooth changes in curvature … topology is any aspect of the shape that does not change when curvature is varied” – hence a donut and a coffee cup are topologically equivalent (in simplistic terms, they both have one “hole”) whilst a sphere and a donut aren’t. And eventually I managed to “get” that the spherical surface of the earth is two dimensional – you only need two co-ordinates (eg latitude and longitude) to locate a point on the surface. But when she started talking about tiling – particularly in 3 dimensions – I must confess I got a bit lost.
However, I’m going to take comfort in the fact that this is the first time (other than simply hearing the word) that I have come across topological concepts, in contrast to the stuff I was understanding which I have mostly encountered many times before. In the past, this lack of immediate comprehension would have bothered me greatly, but when I found the following in a blog entry written by a PhD student last year, I realised that it’s OK to have to revisit concepts before understanding finally dawns:
“From past experience, I've found that if you just immerse yourself in a subject for long enough, the terms and ideas gradually seep into your system.” (Thanks to Gooseania, a blog which I read regularly and sometimes understand)
Until I reached the sections which start talking about topology, I was doing quite well and mostly understanding things. I did understand the difference between geometry and topology, “geometry is about curves and smooth changes in curvature … topology is any aspect of the shape that does not change when curvature is varied” – hence a donut and a coffee cup are topologically equivalent (in simplistic terms, they both have one “hole”) whilst a sphere and a donut aren’t. And eventually I managed to “get” that the spherical surface of the earth is two dimensional – you only need two co-ordinates (eg latitude and longitude) to locate a point on the surface. But when she started talking about tiling – particularly in 3 dimensions – I must confess I got a bit lost.
However, I’m going to take comfort in the fact that this is the first time (other than simply hearing the word) that I have come across topological concepts, in contrast to the stuff I was understanding which I have mostly encountered many times before. In the past, this lack of immediate comprehension would have bothered me greatly, but when I found the following in a blog entry written by a PhD student last year, I realised that it’s OK to have to revisit concepts before understanding finally dawns:
“From past experience, I've found that if you just immerse yourself in a subject for long enough, the terms and ideas gradually seep into your system.” (Thanks to Gooseania, a blog which I read regularly and sometimes understand)
As far as my maths studies go, I’ve finished the year 12 textbook (Maths B) and just have a tutorial, a competency test and an exam to go. So I’m almost ready to send in my enrolment for Physics which I’m really looking forward to getting started on. I’ve also bought old editions of the Queensland Maths C year 11 and 12 textbooks which I plan on going through by myself over the next year or so – it will be interesting to see whether I have the motivation to self-study them without the imposed discipline of having assignments to hand in regularly.
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