21 Jul 2023
I have managed to not post anything here for a whole month. :<
Every night, I am challenged with the question of whether to keep on watching videos on YouTube that I know I’ll forget by the next morning or whether not to sleep. As a big fan of psuedomathematics - mathematics applied in the least non-rigorous setting for the most fun possible - I’m going to try to apply that here. I’ll go over in the end why pseudomathematics is (maybe?) not a complete waste of time.
Getting Started
Assuming everything in your life is predetermined (big assumption, I know) - we can assume the functions of \(life(t)\) or \(l(t)\) is set. This function will return your set of experiences \(e\) each of which can be evaluated for a happiness score \(H(e(t))\) and a memorability score \(M(e(t))\). For now, let’s assume that \(e(t)\) is a vector-valued function with values that are interpretable in the same way of a latent space. The first element of this vector is the time at which this experience starts. Given this, the total happiness in your life \(Q\) from \(t=0\) to time \(T\) over a total of \(E\) experiences
\[Q(T) = \sum_{i=1}^{E} M(e_{i}) * H(e_{i})\]
or with cheesy calculus,
\[Q(T) = \int_{t=0}^{T} M(l(t)) * H(l(t)) dt\]
But we are not done yet! Keep in mind that the memorability \(M(e(t))\) and its happiness \(H(e(t))\) will actually vary throughout your life. An event may be forgotten about but then remembered, or may seem happy at first but then become sad. Not to mention both \(M\) and \(H\) are probably correlated, which we can ignore to make things simpler. For now, let’s revise the calculation of happiness to be for a single experience.
\[Q(e_{i}, T) = \int_{t=e_{i}[0]}^{T} m_{i}(t) * h_{i}(t) dt\]
where the \(i\)th event will have it’s own memorability and happiness functions for each second - \(m_{i}(t)\) and \(h_{i}(t)\) respectively. Because “life is nothing more than experiences” we can just sum up the experiences given by \(l(t)\) at each second.
\[Q(t) = \int_{t=0}^{T} Q(l(t), T)dt = \int_{t=0}^{T} [\int_{s=t}^{s=T} m_{i}(t) * h_{i}(t) * ds] * dt\]
This also means the change of your happiness every second is given by
\[Q'(t)= \int_{t}^{T} m_{i}(t) h_{i}(t) dt\]
Of course this can all be repeated for pain/sadness, which we’ll just assume is the negative of happiness here. But the basic tradeoff of memorability vs. happiness is still there.
Back to the Question
So basically this view of happiness leaves a question of whether its better to have higher happiness and less memorability or vice versa. We’ll look at each case before translating our rationale to math.
Case 1
A situation with higher happiness and less memorability looks like an overworked hedge fund manager choosing to have a year long vacation (at its extreme).
Case 2
The most extreme example of living with no memorability but constant happiness would be partying every single day, watching YouTube every single day, not working a mundane job, etc.
The goal of contemplating this is to understand the behavior of the functions \(m(t)\) and \(h(t)\). Which scenario seems better? Of course, I think most people would choose Case 1 - the common argument would be that Case 2 is aimless and vainful. Both memorability & happiness of a given experience \(i\) decay past that event’s starting time.
It’s also imperative to remember that given the current mathematical formulation, we are trying to maximize happiness greedily as we are only looking at \(Q(t)\) of the current time and not considering long-term effects. This sways much more heavily to case 2 - that happiness leaves slower than memorability.
This actually, does make sense. When going to a restuarant and eating a dish we’ve never seen before we will likely only remember a few things - 2 minutes of conversation, the first time we saw our food, etc. Happiness of eating the dish when we are hungry would last a little longer.
Therefore, I think it’s fair to say that because memorability of an experience after its start date is naturally focused on non-mundane points (beginning, end) whereas happiness of an experience seems to last longer we can rationale that happiness of an event dies down at a lesser power than memorability. Even further, because memorability focused on specific points (1-2% of the actual lifetime), that means that \(m(t)\) is very likely 0. Therefore, counterintuitively we should be optimizing memorability over happiness.
Back to Problem Again
Because \(m(t)\) is going to be 0 a lot more than \(h(t)\), we need to increase \(m(t)\) as much as possible to make \(h(t)\) actually mean something. Therefore uniqueness of experience and variety matters more than feel-good indulgence.
Stop watching YouTube at 4am lol.
Why use Pseudomath
What I just did is a horrible way to solve a problem.
Pseudomath is a continual reminder that math can’t solve all our toughest problems. Problems so hard a book didn’t come with them. Furthermore, if I had not used pseudomath how would I have thought about the tradeoffs of memorability and happiness? Maybe I would have instead said optimizing happiness is better because we only have one life, or that we don’t forget the happy moments in our life.
09 May 2023
Writing this at 4:40am after a day of 3 AP exams. Slept too early.
I’ve been thinking about whether exams make someone a better person. They are stressful. They can corrupt a love for learning.
But they also teach dealing with a stress in a relatively low-pressure, stable environment. The task at hand is extremely well defined, sometimes you are even given a guide to prepare, and nothing (no monetary outcomes) are at risk if you fail. However, for a job - high-stakes situations arise without warnings, unstructured, and can be mired in political capital problems. Thus, are exams the training wheels for adolescents to deal with these times later?
Furthermore, in these exams those who either studied the most, were the smartest, or cheated typically do best. It may feel discouraging to see those who barely studied get an A compared when you worked much harder. Again, not a good reason to <3 exams. But isn’t this also realistic of how performance goes in the career “real-world”?
So to go back to this (argumentative essay) prompt - no, exams don’t make you a better person. Or I could argue that (for me at least), taking hard exams (and doing well on them) does make me more confident to take on harder, stressful challenges. But an N=1 sample is too small to generalize, so I’m going to stick for no today.
The bottom line is that exams are preparation of something more in a heavily controlled environment. And I think it’s going to be a long-time until we can evaluate a person’s skills in a situation that doesn’t involve an exam (e.g. reading their brain flows and chemicals) as accurately. So might as well try to frame tests as something nice for the interim time.
04 May 2023
Purpose
A lot of times in our life, we reflect more on what isn’t going well and not what is. It may feel like everything fails at the worst moment - however, we rarely acknowledge all the things that did go well, or by contrast worked and did not succeed. For example, during a test we will underestimate how many we got wrong because we spent so much more time on questions we didn’t know the answer to. Part of this makes sense though - we expect staples to staples in them, computers to charge when we plug them in, and phones to work (we expect things to work.)
In light of this idea of gratitude, one idea I had was to keep a rolling list of all the things I’ve seen that have luckily gone in a favorable direction. That way, I’ll pay more attention to what is working than just what isn’t.
Lucky Nice Things
- Important Account Online for me has its password, not entire account, expire
- The Test Question did not ask about simulations
- The MCQ was Free
- Only lost a year due to COVID-19
- Practice Tests Haven’t Asked About Holes in a Conductor
- The company I work at doesn’t focus on engineering as much as research
- I was able to conduct an independent project, instead of continue an existing one
- Admin didn’t kick us out even though we didn’t formally sign up to run the event
28 Apr 2023
I know I have not maintained this thing. That is not due to AP exams but laziness.
One thing that’s been on my mind for a while now is why the internet has taken form in the way that it has. Why is United States the country with the highest GDP? Why did they choose a different shade of blue and typeface for different parts of the chapstick container that will be not noticed by 99% of users? Why am I born at this station of status in the world?
Too often, we don’t don’t ask enough questions. There’s a lack of questioning of why the world acts in the way it does and why it arrived at this specific state out of an infinite amount. I’m pretty sure this is because in such a highly structured and organized society, we don’t realize the bigger picture that the single planet we are engrossed in comprises of man-made concepts. The world is deterministic to some extent. I can’t find the eraser at school because I forgot it. It’s not in multiple positions as we may think, it’s in one.
There’s so much for us to question. The Pacific Ocean isn’t real, country lines are imaginary, money has no intrinsic value. So much of the prejudice around us in baseless and crumbles under reasoning of “WHY”? How have humans been able to create fake illusions that now are considered as real as the earth itself? In our origins where we could die at any minute, why do we celebrate birthdays - are we proud to survive another year or cheering away the fact that we are closer to our death :skull:?
Alan Kay: “The Internet was done so well that most people think of it as a natural resource like the Pacific Ocean, rather than something that was man-made”
Furthermore, is pondering the current state of the world even worth it? If scientists are correctly, we are one in infinite parallel universes - just a permutation of what could have occurred over the span of all time. Why debilitate over whether we need to change when life is getting better (overall)? If our world’s state, configuration, policies, whatever is just one in an infinite amount - is it even important?
But if it’s the only one in this shape - can we not also conclude with a 0% p-value that this configuration is sacred in a way? Like, the trajectory of how the world evolves that we are part of is significant (maybe the best, the worst, or some other distinguisher)? With a infinite amount of paths to take, is the road that we have taken special?
I’ve been thinking about this especially after reading Grendel for my school’s APLAC class. In Grendel, the rich dragon criticizes the beast at his ignorance of the world. In particular, he mentions that the fact a certain object (e.g. a jug) has been repeatedly made proves its inherent value; after all it was that particular configuration of atoms (from an infinite set) repeated many times that shows it’s too significant to ignore. Similarly, our policies & ideas may be significant, holy decisions as we continue to practice the same rules again and again, like monetary and fiscal policy.
Nobody knows.
24 Mar 2023
Writing this with a C in APLAC lmao. Now a B. Now an A. lmao.
Our school recently encountered a power outage where we got a good amount time off from school. When the announcement came, I was surprised to see how prevalent the belief that students-must-hate-school stuck (I am somewhat guilty of this, but in my defense it meant I didn’t have a quiz tomorrow). Everybody cheered because there was less school, as if the fact that school was bad was dogma and self-evident. Well, I don’t hate school and thus here this 💩post goes.
Meeting People
No, the first reason is not learning. I am not that corny/predictable (for now).
Despite the striking lack of diversity my 90% Asian high school has, there’s a good amount of varied attitudes and people. It’s not hard to find math nerds five feet away from students blasting music and playing spikeball. As part of going to school, I enjoy chance interactions/conversations and making as many jokes, however degenerate, as possible. Collaborations & opportunities all come from exposure to people outside your “bubble” - I find you only (or at least for me) get that from talking to different people. Futhermore, it’s always interesting to learn about people and what they spend their time on precisely because sometimes I could never imagine myself doing what they do. I will sometimes even pretend that a door is not open just to start a conversation with whoever will open it 💀.
These chance conversations literally whenever - during class, passing periods, walking to and from school - are already a good enough why to go to school. Regardless of how much sleep I got the last night, meeting new faces who eventually become friends makes school worth it.
Shared Suffering
OK, so I’ve been talking about how I like school but now state that in it we suffer? Let me elucidate (as my english teacher says).
Getting screwed week after week with hard tests in tough classes, as far as I’ve seen, generally brings people together. I’ve noticed that the hardest classes usually create the best bonds as everybody tries to prepare for the upcoming test. I would argue that is part of the reason that students actually enjoy harder classes than those easier (assuming it works out for them). For some reason it can be embarrassing to admit, but we do like learning.
Starting with a quick disclaimer that I am in awkward position to praise the American public education school system as a student at a high school ranked in the top 100 in the US and top 10 in California.
But as far as I have seen, most of the information we learn in school is NOT useless. Gaining a broad foundation across disciplines is valuable at an age (<20) where it cannot be expected (in first-world countries) that we should know what we want to dedicate time to. I do think there is value in being able to understand the world around us, which school addresses somewhat completely - how the world formed around us (history), provable truths about our world (sciences), what our world & collective psyche is based on (language classes). It’s not bad.
Conclusion
I’d say most students would happily take two weeks off from school if given the choice but then secretly want to return in a month or so. Would anybody ask to restart school? Idk.