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Repetition......
So still working through the exercises in the Trig book. Trying to avoid the temptation of skipping some is hard, but repetition is key. It’s incredible how many dumb mistakes it’s possible to make upon repetition of the same thing.
I’m feeling impatient, I want to start getting my teeth into the algebra textbook. I know fine that if I start on that i’m just going to end up confusing myself. Bought myself a nice small jotter for portamaths, breaktimes at work will never be the same again! The reaction at work to what i’m doing is one of complete bewilderment and to be honest, I totally get that bewilderment. So....... you’re studying maths........for fun? Cue getting looked at like i’m a fucking serial killer. Maths as a subject among my peer group appears to be one of universal revulsion, the cause of many an adolescent emotional collapse.
Really want to get my head down and finish the Trig book, but unfortunately I don’t get the others until December 25th, so not in a massive rush. Maybe I should start looking at the science behind propulsion specifically as a preamble to phase 1 of the plan, but that’ll be a leap straight into calculus. Maybe some popular science reading as prep......
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Apocalypse soon
I love the smell of trigonometry in the morning. Smells like........ Victory.
Never have I been so happy to be able to understand something. Got the first of my 3 books in the ‘Teach Yourself’ series by Hugh Neill, on Trigonometry. Really good clear explanations thus far, and plenty of exercises to test and repeat what has been learnt. I know it’s GCSE level stuff so far, but i’ve actually understood it and can apply it. Got to use my cheap as chips maths set, wielded a compass and ruler for the first time since my teens and it feels awesome.
I’m preparing for the inevitable though, there will invariably come a point where I stop understanding things. Distractions have been high this week, been off on leave so been utilising the time by mostly being idle and playing Hades. Good game. Trying to convince Mrs. Insanity that a PS5 is a good idea, but probably won’t be able to buy one even if I want to.
Anyway, back to the geometry.
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A mind blowing discovery.
So myself and Mrs. Insanity were watching Top of the Pops 1990 last night, a common pleasure on a friday night here in the UK in these coronavirus addled times. We made a staggering mathematical discovery (and Mrs. Insanity hates maths). We discovered, beyond all doubt, that Elvis - Elvis = Shakin’ Stevens. I mean what the fuck is shakey doing in the charts in the 90′s?
Anyway, current approach to maths is to stop thinking that i’m in any way further ahead than an average 10 year old, and accept that i’m going to need to go back to basics. To that end, I’ve requested books on Trig, Algebra and Calculus for christmas, and have started watching NJ Wildberger’s videos on youtube about the history of maths, taking notes, the full works. Ordered a maths set from Bezos the Billionaire, so a have the means of drawing straight edges and circles in my notes.
So that’s where we’re at, watching TOTP from the 90′s and rocking maths like it’s 1987. And people say middle age is boring.
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Lenny and George enter the fray.
I wish I was reading Steinbeck to be fair. So classical mechanics is another tough cookie, I’m thinking maybe a book for 5 year olds might be a better starting point.
On the plus, I managed to successfully figure out exercise 2 in the book (exercise one was just plotting graphs in Mathematica, easy peasy). It concerned vectors, and mathematical functions. The book tells you how to add vectors by combining them graphically and completing a quadrangle from the 2 vectors, with the diagonal of the quadrangle being the sum of the 2. Then it asks you to figure out how to subtract vectors.
I really wanted to cheat, but didn’t. I actually figured it out on the logic that if the negative of a vector is that vector in reverse, subtracting vectors is the same as adding the negative vector - ie drawing another quadrangle. go me!
It all went tits up from there. I watched Leonard Susskind’s accompanying lecture, and was doing alright until he started talking about expressing the movement of particles on vectors as a derivative of time. He said if you don’t know what that is you’re probably in over your depth. Shit. So new goal - Calculus.......
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The real first stumbling block.
So I went back and reread the book starting at chapter 2. This being the chapter where maths is first discussed. I wanted to find the exact point where I lose what’s being said.
Hyperbolic geometry is our winner. Penrose uses an artwork by MC Escher to describe the basic principle of hyperbolic geometry.
This one. So this is a Euclidean representation of a hyperbolic space, the small figures are only small because they are at the limit of the 2D bounding circle, they are in reality the same size. And all those circle sections are straight lines in the hyperbolic plane. And apparently it’s relatively simple to do the geometry of hyperbolic triangles.
Apparently.
It mystifies me. Maybe my latest purchase, Classical Mechanics - The Theoretical Minimum, will boost my mathematical thinking.
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I Need a Plan
So i need a plan. I need something to aim for. Intermediate goals are important.
The visit to Amazon was fruitful, a new book was purchased: Classical Mechanics: The Theoretical Minimum. Seems like this one is going to give me more of a challenge than The Joy of X. Pre-emptively ordered 3 A4 jotters and a pack of 10 pencils, we’re going IN.
Well, just as soon as it arrives anyway.
So yeah, a plan is needed. Motivation. Of course the main motivation has been stated, I want to understand The Road to Reality. This isn’t going to happen overnight though, and i need to actually apply some of the stuff i’m going to learn in order to learn it. So what can i set as an intermediate goal? Moon landing, totally got to be moon landing. How the fuck am I going to understand the mechanics of the cosmos if I can’t even manage a simple moon landing?
Unfortunately, I do not possess the bank balance of Elon Musk. Fortunately, I do have a copy of Kerbal Space Program. So the intermediate goal is set, Mun mission in Kerbal, but don’t do anything that I can’t explain with maths. Awesome! That’s probably going to take a year or more. Yay. Rockets.
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An Early Humbling....
So I got a few chapters in.
It started to properly lose me when it hit complex numbers. Nearly 400 pages of this book is maths and I’m stuck early. Shit.
To be fair, grasping i2 = -1 is probably beyond a lot of people. Managing actual numbers is hard, and now they add imaginary ones 🙄.
On the plus, Penrose writes well. Only trouble is he doesn’t always clearly explain for the newbs what he’s doing when he manipulates equations. Or maybe it’s just that I’ve not done any real maths for 25+ years and I’m rusty. In any event, we need a reminder - off to Amazon’s algorithm again!
This time, we need stuff explained, we need a grasp of the basics before handling Penrose. I went for ‘The Joy of X’ by Steven Strogatz. Highly recommended, hilarious in places. Read it in a day (pew pew). Downside though, it falls into the category of the popular science books I’d read before - it explains the concepts and why the maths works, but doesn’t ask you to apply it so it’s more an interesting romp through maths as a subject but not too helpful if you want to learn how to do differential calculus.
Jesus. Why the fuck do I want to learn differential calculus?
Anyway, back to Amazon. Other outlets are of course available.
Edit: must try to find out how to do notation on here. Like my to-do list isn’t long enough.
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Beginnings
So, my Dad died. Which was sad obviously.
When writing my portion of his eulogy, I mirrored his belief in lack of a divine creator, instead preferring to believe in science. I’ve long held fascination with all of the sciences, I work in the field of medicine (albeit in a supporting capacity). When writing the eulogy I came to realise that I believe these things, and I trust the scientific method behind them, but I don’t understand them. I don’t understand the key concepts of physics, particularly not on a mathematical level.
Thus, the adventure begins.
I decided that I wanted to rectify this. As I said, I’ve been interested in this particular branch of science for a while, and have read a lot of popular science books, love listening to the wonderful ‘Infinite Monkey Cage’ on radio 4 and have a grasp of the broad concepts. With this in mind, I set my sights on a book that would fill in the gaps, would give me much deeper insight into the mathematical basis of all these concepts. I settled (based on amazon’s algorithms and the fact that my dad owned a copy) on ‘The Road to Reality’ by Roger Penrose.
This should be fun. Said no sane human in history.
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