Linear algebra for an exponential life
#150 - a Bank Holiday bonus: an exam the next day
Hi there,
When the mind is focused on one thing, necessarily, it isn’t focusing on other things. It isn’t spending time ‘in the clouds’. And hence it doesn’t pick up on curious phenomena or thought-provoking ideas, which translate themselves into a blog post.
And then, #150 doesn’t happen. The train leaves the station, but doesn’t get to the next one (particularly when it’s weighed down by a sickening cold).
Hello - it’s been 2 weeks of a lot of maths. The outcome is certainly that I am much more prepared for the exams to come. At least it’s been wonderful outside, making the little time I can afford to relax outdoors (or lug the whole of ASDA home - they’ve stopped deliveries when I most need it!) magical. What’s also magical, I reckon, is what I’m writing about today - a special for our 150th date together 😄
Highlight of the week: not much to write home about this week. The weather has certainly been up there, the Sun has definitely been Out! 😉I did manage to catch one evening when it wasn’t, yet it still looked stunning
Let’s get into the Ray of Sunlight: been looking forward to this one all week.
My first exam is linear algebra: the study of vectors (in essence, lists of numbers), matrices (tables of numbers) and linear transformations (changing between these). Let’s go for a maths lesson that will be the basis1 of my thoughts today.
We have these structures called vector spaces. I won’t bore you with the 9 criteria they must follow, but think of a vector space as a big bag of fruits - they are special sets.
Each fruit has a few basic characteristics - its colour, does it need to be peeled, the countries it’s grown in, its nutritional content, whether it needs to go in the fridge…you get the gist. A basis for a vector space is a subset of the vector space from which you can build the rest of the elements.
A more mathematical example would be all of the points on a 2D plane, your standard x and y-axis. Every point (x,y) can be written as x * (1,0) + y * (0,1): some multiple of a ‘unit vector’ in the x-direction and y-direction.
There’s the maths you need to know, to now make sense of the post. If only all of university maths was so simply explained in a language I understand (food). 😁
I have realised that sleeping, studying and living in a single room is not optimal for productivity. I sheepishly scan my desk and realise that the lack of clean space doesn’t help… 🙈, but I knew that I just wouldn’t be at my best doing full past papers up here in my room. A quote from Think Like a Monk by Jay Shetty comes to mind:
Location has energy; time has memory… To watch Netflix and/or eat in your bedroom is to confuse the energy of that space. If you bring those energies to your bedroom, it becomes harder to sleep there. Even in the tiniest apartment, you can dedicate spaces to different activities. Every home should have a place to eat. A place to sleep. Create spaces that bring you the energy that matches your intention.
I take a trip down to the study room, and there’s space (a normal space, not a vector space here 😉) for me (unexpected during exam season) and I set up for a long haul.
3 hours later, I have successfully completed my first ever 3 hour university maths past paper. I sit back, looking out of the window at a couple sipping on their chilled drinks in the summer weather and the replete2 trees dancing away, and realise: that’s the first time I’ve done 3 hours of maths since the infamous STEP 3 on June 24. How much life has changed since.
As though moving through a mindfulness exercise, moving from the outside world to the space (no, I won’t make the same joke again, that would make my comedy too basic) around me, I notice the guys around me who have been there for long periods of time, one even longer than me.
It made me think about the mental limit I have set myself, with regards to my ability to concentrate. Backed by the theory of the Pomodoro technique - studying for 25 minutes, then a 5 minute break (or scaled to 50, 10) - and the belief that university maths is too mentally intensive to concentrate for longer than 45/50 minutes, I haven’t had too many ‘study sessions’ longer than an hour without a break over my 2 and a bit terms at university so far (as my Toggl Track would prove - more on that here).
However, being able to sit still for 3 hours and do a paper and, furthermore, see others study for long periods of time disproved that logic. It is a new basis vector that I can build my life with. My time at university so far has seen my mental world of possibilities expanded - new basis vectors for the most exciting vector space of them all, what’s possible to accomplish - by meeting many people.
A friend who has plans to drop out of Imperial, the proudly 2nd best university in the world, but with good reason - £50k+ start-up jobs lined up… as a 19 year old
A flatmate who, as an antithesis to the typical Gen Z-er, let alone university student, goes to sleep at 9:30, eats well, goes to the gym, studies hard and doesn’t listen to music.
A friend, also my age, who is earning well over £20k a month from sales calls and other cool projects he’s involved in.
A friend who sleeps late, wakes up late, plays video games and surfs the Internet most of the day and still does better than me in the exams.
Yes, these might be the tail-end examples, but that’s precisely the point. What each of one of these examples does is to shatter the ceiling and your pre-conceptions of just what’s possible.
Here is where I reach our main point today - one of the most important jobs in life is to be constantly growing the size of our basis set, expanding what we realise to be possible. Whilst linear algebra says that bases of a finite-dimensional vector space have the same size, I believe we are living in an infinite-dimensional vector space. Your basis can be as large as you want it to be - and I’d rather have a larger basis, so I can access more of the world, aim for more in the world and ultimately, be able to understand a larger portion of the vector space we call ‘life in our world’.
It has been a while since I’ve enjoyed a post so much. Perhaps it’s having my head buried in maths all week, and hence the lease of freedom writing in English (although Maths is more letters than numbers these days…) and snack of creativity (the food analogy continues!) that the blog offers me. Nevertheless, I hope you enjoyed reading this week as much as I enjoyed writing it.
Podcast of the week🎙️
The Diary of a CEO: Michelle Obama
A no-brainer choice this week. Such a fluent, engaging conversation - and one I will definitely need to revisit when I’m out of the woods. Highly encourage you give it a listen or watch.
What I’m grateful for this week 🙏
The ASDA staff who were very much ‘happy to help’ me find stuff when I went to the store this weekend
Quote of the week 💬
However difficult life may seem, there is always something you can do, and succeed at - Stephen Hawking
Let’s hope Hawking was talking about my exams. I might see you next week. If not, maybe time for a repost of one of my favourites? Keep working hard, everyone - summer’s getting closer.
Adi
This will make sense upon 2nd reading
I learnt this word this week - filled or well-supplied with something.