I study decision theory but I have trouble making them.
Also a very informal introduction to complexity theory.
This post has footnotes to talk about things which are just offhand comments or technical details. You can feel free to ignore them or read them, you do you.
For all my academic life, there are two things I know: I am good at math and that I want to become a doctor.
This was rather a paradoxical position to be in. In India, if you are considered 'smart' or 'gifted', you are asked to choose between biology or math. If you choose biology, you become a doctor; otherwise, you become an engineer. You can understand the paradox.
But in the final year of school, I decided I didn't want to become a medico. I didn't want to spend a life remembering and recalling names of symptoms and matching them with diseases and then with medicines.
Even worse, do that without ever understanding why the symptom matches with the disease and why the medicine works. Like doctors do learn pathology for some common diseases but not entirely. And then again, why would they? Diseases are studied by microbiologists, virologists, and immunologists; drugs are created and tested by molecular biologists, geneticists, and pharmacologists; the drug tests are created by biotechnologists and bioinformaticians; and the spread of diseases is studied by epidemiologists.
Not to understate their contributions, doctors do use these results to help us. But they don't understand these papers or the methods to do this research themselves.
I used to believe doctors made the vaccines and the pills and designed the tests. Naïve, I know. So once I started to realize this, I started to feel that becoming a doctor is memorizing a large and complicated; but ultimately pre-determined lookup table.
So I decided to switch to math. But then I didn't want to become an engineer.
Again, nothing against engineers, but I don't want to spend a life implementing algorithms I don't understand. Like I want to make algorithms, I want to ask if we can do better and when we can't, why? Why are some problems hard and others easy?
So I decided to go into research. This disappointed a lot of people.
But this was an easy decision to make.
Over my first semester, my main interest of research became decision theory.
Decision theory, at the heart of it, is the math of modeling real-life scenarios and optimizing decision-making. It deals with financial markets and elections, fairness and moral hazard, auctions and corruption; everywhere a decision is to be made, decision theory enters.1
Now here's the thing, (I think) I am decent at decision theory. I understand most theorems. Can prove most of them in a bling. I also have some idea of the limits of the subject but then I don't understand why taking some decisions is harder than others.
The entire above decision, the switch from bio to math didn't take more than a few days. But I am writing this on an old HP Pavilion which has a blown out 'G' key and a barely functional down arrow. And a trackpad that doesn't work. And a battery that doesn't work so I am forced to keep it plugged in.2
So I have to get a new laptop. And I have been trying to decide on one for almost an entire month.
Should I get a gaming laptop? What even is a gaming laptop? Is that just a buzzword to charge more money?
What is a professional laptop? Do they wear a tie and a suit and speak in a British accent?
Are Lenovos even good? Is Asus sus? Is Acer ace? What is ROG?
What do you mean by OLED display? What does a better GPU mean for me? Why are there SSD and RAM types?
And then there is the brand repute. MacBooks are too expensive. Also, I don't like macOS. HP has a reputation for bad battery and motherboards.
And then came the reviews. I normally only recommend Reddit for reviews as that's the one place completely free from affiliate and paid marketing. But Reddit confused me. What do you mean 'Victus 2023' was good but '2024' isn't? Like did the production get worse or did better laptops come up? Also, why are laptops priced differently in nations? Why is a laptop 239 USD in USA and 800 USD in India? What is the difference?
With a lot of research, and thanks to JustJosh, I shortlisted Lenovo Yoga 7i, Asus TUF F15, and Acer Aspire.
So I decided to visit Croma, Vijay Sales, and Reliance Digital, which are Indian versions of Best Buy.
And I was confused further. TUF was too heavy. Aspire and Lenovo were good but the former is cheaper. But the former is more powerful. Now see, they ask me to 'test' it out in-store. But do I then install and set up a Haskell development environment?
Also, now Asus Vivobook got added to this list. The salespeople kept trying to sell me on Lenevo as it (allegedly) had more service centers in India than Acer and Asus.
I come home with this confusion. My father advises me to ask the other people through the university WhatsApp group.
Some people recommend Asus. Some recommend Acer. Some recommend Lenovo. Some don't understand budget and say Legion. Some say HP, and (HP) gets dunked on by everyone else.
And this is further sending me spiralling.
Like I didn't take much effort to make a career decision but to choose a laptop, I am more confused than ever. Like in decision theory, ideal decision is one which maximizes utility or minimizes future regret.
But what is utility of say 'TUF F15' or 'MacBook M3'? What is even the probability distribution of utility? What is the regret function if say I am unable to work on ‘Zenbook’ ?
I also have the same confusion while choosing ice creams. Like, more often than not, I just take Amul chocalate or cookie cone or any vanilla Ice Cream Sandwich. But I feel almost paralyzed when these are not available. As if I don't know what I want.
This confuses me. Why are these problems so complex?
In CS, given a problem, we can decide if it is ‘easy’ or ‘hard’. This is called Complexity Theory.
While I'm not very proficient at Complexity Theory, this problem seems to be NP (please excuse this Gell-Mann Amnesia inducing definition: It is a formal way of saying quite hard).
I'll reiterate, I don't understand complexity theory very well and nor is this a formal proof. However, I have a lot of conditions if a laptop is 'good' like 8 GB RAM with a GPU works but 8 GB RAM without GPU is not okay. So it's a function which takes a bunch of booleans(read ‘yes/no’ or ‘true/false’) as input and there are a bunch of ways to relate them, aka operators, to get a single boolean representing if the laptop is ‘good’. This means my laptop choice problem reduces to the satisfiability problem which is known to be NP. Even strongly, it is known to be NP-complete. That is, if you solve it, you can solve any NP problem. So if you help me choose a laptop, I will help you hack into anything (breaking encryption is NP).
Coming back to the laptop issue, my main problem is that I am getting no good advice with respect to getting a good laptop. As any advice will help me choose the laptop and solve my NP problem, giving any useful advice is NP-Hard.
NP-Hard is a formal term meaning solving the problem would solve an NP problem. And in CS, we already know that solving an NP-Hard problem is as hard as solving an NP problem.
Now, if we continue with this CS metaphor, there are Approximation algorithms. These are P (read 'easy') to solve problems which provide an approximate solution. Sometimes, these Approximation algorithms basically solve the problem for all practical purposes. Other times, they just exist for our theoretical fun.
In my case, the approximation algorithms aka ‘general’ advice are useless.
Learned people have told me versions of: Get a good RAM, processor is prime for programming, good screen means good leisure time, without battery you won't be able to use the machine. Like I didn’t know…
All this theory aside, the thing bugging me, is that choosing a career should be much more complex (or atleast equally complex) than choosing a laptop. The former has many more dimensions.3
Yet, here I am writing this on the HP with the busted G.
While I have no paper to publish, or even a conclusion in that regard, it seems to me that it is easier to make choices which don't affect me in the short term.
The consequences of choosing a bad laptop are almost immediate. A noisy fan and I can hear the professor shouting 'Shut the laptop'. Heavy body and I can imagine my shoulder aching.
Same with ice cream. I can imagine the vomit inducing gag or the satisfying 'ah!' of the treat I am about to buy.
But with a career choice, I really can't imagine much. The choices in one way, don't affect me. They affect future me. And while the rational assumption is that both are equal, the distance of the choice and utility make the decision easier.
When I started decision theory, I thought it would make me better at making decisions. But alas, the developers of StockFish are not GMs and nor am I good at taking decisions.
Perhaps the most rational choice is to realize that there is no perfect choice and sometimes we must just make an approximate choice. After all a good-enough choice is exactly what it says it is, good enough.
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If you have any (non-trivial) advice to add to the bag, feel free to drop into the comments.
Of course that's not all. Case in point: My first semester student seminar was titled "Bubbles that Burst: Why markets rise, fall and who comes out on top?". It was a game theoretic analysis of financial bubbles. But then again, we were not making a decision on when to enter the market, or what bubbles to invest in. We are just trying to analyze how (ir)rational one needs to be to invest in a market at a particular moment. Why people make the decisions they make and what effects that causes.
It's technically a problem with the CMOS checksum. CMOS basically stores a lot of critical low-level data, like date and time and boot settings and (importantly) battery data. The CheckSum makes sure this data is not corrupted by, say a virus, as these are critical things. As my CheckSum has failed, my laptop cannot tell how much battery it has. At least in my laptop, 'mystery' battery amounts are taken as 0 battery.
Literally. We can determine the utility function of a choice as the norm of the utility vector where the utility vector is the score the choice gets on some set of categories. Like taste in case of ice cream and opportunities, enjoyment, compensation and a lot more in the case of carrer.